4/15/2015HW10: Chap 17.5,17.7, Chap. 18.418.6 HW10: Chap 17.5,17.7, Chap. 18.418.6 Due: 11:59pm on Thursday, April 16, 2015 You will receive no credit for items you complete after the assignment is due. Grading Policy Heat versus Temperature The specific heat capacity of aluminum is about twice that of iron. Consider two blocks of equal mass, one made of aluminum and the other one made of iron, initially in thermal equilibrium. Part A Heat is added to each block at the same constant rate until it reaches a temperature of 500 K . Which of the following statements is true? Hint 1. How to approach the problem Heat is added to both blocks at the same constant rate. That is, the same amount of heat is added to each block per unit time. Therefore, the block that reaches the final temperature in the smallest amount of time is the block that requires the smallest amount of heat to undergo the given temperature change. Since both blocks have the same mass and undergo the same temperature change, you can relate the amount of heat absorbed by each block to the block's specific heat capacity. Hint 2. Specific heat capacity Given a sample of mass m of a certain substance, the amount of heat Q needed to change its temperature by an amount ΔT is given by Q = mcΔT , where c is the specific heat capacity characteristic of that substance. It follows that the specific heat capacity c of a sample is the amount of heat required to raise the temperature of one gram of the sample by 1 K . Hint 3. Identify which material requires more heat Consider several onegram samples of different materials. Heat is added to each sample to increase its temperature by 1 K . Which material will absorb the most heat? Hint 1. Definition of specific heat capacity The specific heat capacity c of a sample is the amount of heat required to raise the temperature of one gram of that sample by 1 K . ANSWER: The material with the smallest specific heat capacity will absorb the most heat. The material with the largest specific heat capacity will absorb the most heat. All the materials will absorb the same amount of heat because they all have the same mass. All the materials will absorb the same amount of heat because they all undergo the same change in temperature. https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 1/21 4/15/2015 HW10: Chap 17.5,17.7, Chap. 18.418.6 ANSWER: The iron takes less time than the aluminum to reach the final temperature. The aluminum takes less time than the iron to reach the final temperature. The two blocks take the same amount of time to reach the final temperature. Correct Part B When the two materials have reached thermal equilibrium, the block of aluminum is cut in half and equal quantities of heat are added to the iron block and to each portion of the aluminum block. Which of the following statements is true? Hint 1. How to approach the problem Since the same quantities of heat are added to samples that have different masses and different specific heat capacities, this may result in different final temperatures for each sample. However, you must keep in mind that each smaller block of aluminum now has half the mass of the iron block, but about twice the specific heat capacity. To solve this problem use proportional reasoning to find a relation between ΔT , c, and m. Find the simplest equation that contains these variables and other known quantities from the problem. Write this equation twice: once to describe ΔT i , ci , and mi and again to relate ΔT a , ca , and ma , where the subscript i refers to iron and a to aluminum. Write each equation so that all the constants are on one side and the variables are on the other. In this problem the variable is ΔT so write your equations in the form ΔT = ⋯ . Finally, compare the two cases presented in the problem. For this question you should find the ratio ΔT i /ΔT a . Hint 2. Find the temperature change of the iron block When an amount of heat Q is absorbed by the block of iron, what is its change in temperature ΔT i ? Use m i and c i for the mass of the iron block and the specific heat capacity of iron, respectively. Express your answer in terms of mi , ci , and Q . Hint 1. Specific heat capacity Given a mass m of a certain substance, the amount of heat Q needed to change its temperature by an amount ΔT is given by Q = mcΔT , where c is a constant, called specific heat capacity, characteristic of that substance. ANSWER: https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 2/21 7.6 ΔT i = Q m i ci Hint 3. ci . ANSWER: ΔT a = Q m i ci ANSWER: The three blocks are no longer in thermal equilibrium; the iron block is warmer. The blocks remain in thermal equilibrium. what is its change in temperature ΔT a ? Express the mass of the block in terms of the mass of the iron block mi and the specific heat capacity of aluminum in terms of the specific heat capacity of iron ci . and Q .4/15/2015 HW10: Chap 17. The formula governing this is dQ CH dt = kC A( T H −T C L ). Express your answer in terms of mi .masteringphysics. Part A This formula applies to ________________. Correct Understanding Heat Conduction Learning Goal: To understand the heat conduction formula and the variables in it. Conductionthe flow of heat from a hotter object to a cooler object or from a hotter region to a cooler region of the same objectis the most common mechanism of heat transfer.418. Find the temperature change of the smaller aluminum block When an amount of heat Q is absorbed by the block of iron. Hint 1. ANSWER: https://session. The three blocks are no longer in thermal equilibrium; both the aluminum blocks are warmer.5.17. 18. Specific heat capacity of aluminum Recall that the specific heat capacity of aluminum is about twice the specific heat capacity of iron.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 3/21 . Chap. 5.17.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 4/21 . rod.7. Indicate whether the following statements are true or false.6 any object of crosssectional area A; length L; and thermal conductivity k C any object of crosssectional area A; length L; and thermal resistivity k C a plate of surface area A; long dimension L; and thermal conductivity k C a plate of surface area A; long dimension L; and thermal resistivity k C Correct This formula gives the heat conducted at steady state by any object of uniform heat conductivity and cross sectional area. Imagine that you are applying the heat conduction formula to a rod that is held at a high temperature on one end and at a low temperature on the other end. ANSWER: true false Correct Part C The quantity dQ CH /dt is the rate of heat added to the hot end of the rod to maintain its temperature. ANSWER: true false Correct Part D The quantity dQ CH /dt is the rate of heat removed from the cold end of the rod to maintain its temperature. Part B The quantity dQ CH /dt is the rate of heat transfer from the hot to the cold end of the rod. ANSWER: https://session. Typical examples are a wire. whose hot and cooler ends are at T H and T C . 18. or an insulating layer. the latter of which will typically have a large area A and relatively short length (thickness) L.418. respectively. Chap.masteringphysics.4/15/2015 HW10: Chap 17. masteringphysics.7. Part F In the SI system of units. Assume that the thermal conductivities of copper and steel are given by kcopper = 385 W m⋅K and ksteel = 50. ANSWER: true false Correct The flow of heat into. The heat conduction formula applies only in steady state; it does not apply to the situation in which one end of a bar is suddenly placed in a flame while the other end is held at fixed temperature (as in an ice bath); the formula would only apply after the temperature at every point in the bar had reached a steadystate value. insulated to prevent heat loss along its sides.17. through. https://session.2 W m⋅K . 18. Chap.00 m section of copper (with one end in the boiling water) joined endtoend to a length L2 of steel (with one end in the ice water). and out of the rod are equal under steady state conditions in which the temperature of each end of the rod is constant.418. The rod consists of a 1.00 cm2 .0∘ C after a steady state has been reached. The temperature of the coppersteel junction is 65.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 5/21 .5. Both sections of the rod have crosssectional areas of 4.4/15/2015 HW10: Chap 17.6 true false Correct Part E The quantity dQ CH /dt is the total amount of heat transferred from the hot to the cold end of the rod. what are the units of the quantity dQ CH /dt? ANSWER: joules amperes watts Correct ± Heat Flowing through a Sectioned Rod A long rod. is in perfect thermal contact with boiling water (at atmospheric pressure) at one end and with an icewater mixture at the other . which is finally equal to the heat flowing into the ice water. respectively. How to approach the problem Because the length of the steel section of the rod is unknown.5. the length and crosssectional area of the rod in contact with each side and k is the thermal conductivity of the rod.7.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 6/21 .masteringphysics. Because a steady state has been reached. Part B https://session. the heat flowing out of the boiling water must be equal to the heat flowing through the copper section. Equation for heat conduction The heat current through a rod is H = Q Δt = kA T hot −T cold L . ANSWER: H = 5.17. which is equal to the heat flowing through the steel section. Hint 2. where L and A are. Chap.418.6 Part A How much heat per second H (= Q Δt ) flows from the boiling water to the icewater mixture? Express your answer in watts.4/15/2015 HW10: Chap 17. Hint 1. Instead. calculate the heat flowing through the copper section only.39 W Correct Because the system is assumed to have reached a steady state. 18. the heat flowing out of the boiling water must be equal to the heat flowing through the copper section of the rod. the equation for the heat conduction cannot be set up directly between the boiling water and the ice water. which depends on the material used to make the rod. since the junction temperature is known. Part A This formula applies to _______________. How to approach the problem In Part A. 18. the heat flowing through the copper section must be equal to the heat flowing through the steel section. Every object at absolute (Kelvin) temperature T will radiate electromagnetic waves. Kelvin temperature T . You also know the temperatures of both ends of the steel rod. and emissivity σ any object of crosssectional area A. you found the heat current through the copper rod.7.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 7/21 . and emissivity σ https://session. ANSWER: L2 = 0. which is also equal to the heat flowing into the ice water.418. with some visible light emitted for objects heated above 1000 K .242 m Correct Extending the analysis from the first part. Kelvin temperature T . and emissivity e any object of total surface area A.5.17. Chap. since a steady state has been reached. The formula governing the rate of energy radiation from a surface is given by P = eσAT 4 . Use these values in the heat current equation to calculate the length of the steel rod. ± Understanding Heat Radiation Learning Goal: To understand the formula for power radiated in the form of electromagnetic energy by an object at nonzero temperature. we see that. Hint 1. ANSWER: any object of total surface area A.4/15/2015 HW10: Chap 17.6 What is the length L2 of the steel section? Express your answer in meters. where P is the thermal power (also known as the heat current H ). This radiation is typically in the infrared for objects at room temperature. which is the same as the heat current through the steel rod. Kelvin temperature T .masteringphysics. Kelvin temperature T . and emissivity e any object of crosssectional area A. Which of the following alternatives seems to explain this conundrum best? ANSWER: The box is black only in the visible spectrum; in the infrared (where it radiates) it is quite shiny and radiates little power. a square box that is 1 m on each side and painted black (therefore justifying an emissivity e near unity) emits 2.masteringphysics. The StefanBoltzmann constant is σ = 5. and what property of the filament? ANSWER: thermal radiation emissivity length Correct Part C If you calculate the thermal power radiated by typical objects at room temperature. the StefanBoltzmann constant.5 kW at a temperature of 20∘ C . https://session. and c is the speed of light.6 Correct In the formula given. e is the thermal emissivity. several kilowatts typically. Both of the first two factors contribute significantly.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 8/21 .5 kW of thermal energy into the box.418. you would have to know the temperature (determinable from the color of the light). or else the box would cool off quite quickly.0 for a truly black object and varies down to about 0. h is Planck's quantum of angular momentum (or Planck's constant). Neither of the first two factors is the explanation. the power input. Part B If you wanted to find the area of the hot filament in a light bulb.02 for a shiny goldplated object. In reality the net thermal power emitted by such a box must be much smaller than this.5. giving σ= 2π 5 4 kB 3 15h c 2 . The surrounding room is near the temperature of the box and radiates about 2. you will find surprisingly large values. For example.4/15/2015 HW10: Chap 17.7. Its prediction from first principles was the first major triumph of quantum mechanics. Chap. The emissivity is 1.17. where k B is Boltzmann's constant. 18.67 × 10 −8 2 W/m /K 4 and is a constant of nature. 6 Correct Part D As a rough approximation.300kg of water. Express your answer in terms of the StefanBoltzmann constant σ. ANSWER: P = eσAT 4 ANSWER: P = 460 W Correct Exercise 17.418.6 .5∘ C to 86. and any constants.8 m . and the emissivity e . Find the area of the person Find the area A of the person. Express the area in terms of L.masteringphysics. Hint 1.17.0∘ C ? https://session. and the surface temperature is taken to be ∘ T = 30 C . the body area A.5.) If the emissivity of skin is taken to be e = 0. C . ignore the circular top and bottom of the cylinder.0 m and circumference C = 0. the human body may be considered to be a cylinder of length L = 2. how much thermal power P does the human body radiate? Express the power radiated numerically; give your answer to the nearest 10 W . Chap.7. (To simplify things.4/15/2015 HW10: Chap 17. and just consider the cylindrical sides.26 In an effort to stay awake for an allnight study session.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 9/21 . the body temperature T . a student makes a cup of coffee by first placing a 200W electric immersion heater in 0. ANSWER: A = LC Hint 2. 18. Find a symbolic expression for the power Find the total power P radiated by the person. Part A How much heat must be added to the water to raise its temperature from 21. Kinetic theory and statistical mechanics provide a way to relate molecular models to thermodynamics. Cv . Kinetic theory tells us that the temperature of a gas is directly proportional to the total kinetic energy of the molecules in the gas. ANSWER: t = 405 s Correct Degrees of Freedom Thermodynamics deals with the macroscopic properties of materials.11×104 J Correct Part B How much time is required? Assume that all of the heater's power goes into heating the water. Chap. determine by how much the total energy of a gas increases when its temperature increases by one degree.418. determine the molar specific heat. where R = 8. where n is the number of moles of gas.7. The molar specific heat Cv of a gas at a constant volume is the quantity of energy required to raise the temperature T of one mole of gas by one degree while the volume remains the same. How to approach the problem The molar specific heat of a substance is the amount of energy required to increase the temperature of one mole of the substance by one degree Celsius. Express your answer in terms of R and s .6 ANSWER: Q = 8.5.17. Mathematically.314 J mol⋅K −23 J/K . of a gas in which each molecule has s degrees of freedom. Part A Using the equipartition theorem. this gives is the ideal gas constant. Predicting the heat capacities of gases at a constant volume from the number of degrees of freedom of a gas molecule is one example of the predictive power of molecular models.4/15/2015 HW10: Chap 17. Cv = 1 dU n dT .38 × 10 nRT . The equipartition theorem says that each degree of freedom of a molecule has an average energy equal to 1 2 1 2 kB T . When summed over the entire gas. and dT is the change in temperature. dU is the change in internal energy. Hint 1. Scientists can make quantitative predictions about these macroscopic properties by thinking on a microscopic scale. 18. Then apply the formula given https://session. where k B is Boltzmann's constant 1.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 10/21 .masteringphysics. Using the equipartition theorem. for each molecular degree of freedom. By the equipartition theorem.5 1.6 in the problem introduction for Cv . kinetic theory and the equipartition theorem do a good job of predicting the specific heat of many gases at room temperature as shown in the chart below. where the bonds between atoms can vibrate back and forth like a spring being compressed and released as well as possible sidetoside swinging motion from the bonds bending. Hint 2. https://session. A monatomic gas has three degrees of freedom. the energy in each degree of freedom changes by an amount dU 1 = 1 2 nR dT .17.4/15/2015 HW10: Chap 17.03 6 For a monatomic gas.50 3 Helium (He) 12.7 2.418. Part B Given the molar specific heat Cv of a gas at constant volume. Diatomic molecules and linear molecules have three translational degrees of freedom and two rotational components to the motion (rotation about the axis of the molecule does not contribute much except at high temperatures).50 3 Carbon Monoxide (CO) 20.92 3.24 3. when the temperature of the gas changes. Nonlinear molecules have three translational and three rotational degrees of 6 2 R. so Cv is about 3 2 R . Recall that a change in temperature reflects a change in the amount of energy associated with each degree of freedom.49 5 Hydrogen (H2) 20. one for each of the three Cartesian directions.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 = 70.7.6 J 11/21 .5 1. giving Cv a value of about freedom.51 5 Hydrogen Sulfide (H2S) 25. Monatomic gas: an example The molar specific heat for a monatomic gas is 3 2 R. 18. which gives C v 5 2 = R . Molecule Cv J mol⋅ ∘ K Cv /R Degrees of Freedom Argon (Ar) 12. The vibrational motion does not normally contribute to the degrees of freedom until a high temperature of 400 degrees Celsius or more is reached.9 2. ANSWER: Cv = s 2 ( R) J mol⋅K Correct Experimentally. Chap. you can determine the number of degrees of freedom s that are energetically accessible.45 5 Nitric Oxide (NO) 20.4 2. there are only three translational degrees of freedom.12 6 Water Vapor (H2O) 25. Polyatomic molecules also have vibrational degrees of freedom.5.masteringphysics. This histogram shows a theoretical distribution of speeds of molecules in a sample of nitrogen (N2 ) gas.418. However.6 For example. The gas molecules exert no longrange forces on each other. In this problem. The gas molecules are in continual random motion with collisions being perfectly elastic.7. v rms . A relationship between the microscopic properties of the gas molecules and the macroscopic properties of the gas can be derived using the following assumptions: The gas is composed of pointlike particles separated by comparatively large distances.6 degrees of freedom of cis2butene are energetically accessible? J mol⋅K . Hint 1. The rms speed is a good approximation of the the typical speed of the molecules in a gas. the average squared velocity. you derived an equation for Cv in terms of the number of degrees of freedom s .masteringphysics. Chap. this measure does not average to zero over the entire gas. has molar specific heat C v = 70. Substitute known quantities into that equation and solve for s .5. The most obvious measure is the average velocity ⃗ v avg .4/15/2015 HW10: Chap 17. C 4 H8 . 18. at room temperature cis2butene.17. Since the square of velocity is always positive. How to approach the problem In Part A. you'll use the histogram to compute properties of the gas. There are several different ways to describe statistically the average velocity of a molecule in a gas. since the molecules in a gas are moving in random directions. https://session. equal to the square root of (v 2 ) avg . the average velocity is approximately zero. One of the most important microscopic properties of gas molecules is velocity.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 12/21 . How many Express your answer numerically to the nearest integer. ANSWER: s = 17 Correct ± The Speed of Nitrogen Molecules The kinetic theory of gases states that the kinetic energy of a gas is directly proportional to the temperature of the gas. A third measure is the rootmeansquare (rms) speed. Another measure of velocity is (v 2 ) avg . 6 Part A What is the average speed v avg of the molecules in the gas? Express your answer numerically to three significant digits. The quantity v rms is more common than (v 2 ) avg because it has the dimensions of velocity instead of the lessfamiliar velocitysquared.418. ANSWER: v avg = 474 m/s Correct Part B Because the kinetic energy of a single molecule is related to its velocity squared. https://session. More on computing the average To find the weighted average.masteringphysics. Compute the weighted average speed.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 13/21 . Hint 1. or its square root v rms .17. Take the central speed value of each bin as an estimate of the speed of all the molecules in that bin. 18. Hint 2. Chap. adding the results. How to use the histogram The histogram shows the fraction of molecules that have speeds within each of a set of ranges. using the percentage of molecules in a bin as the weighting factor for that bin. Repeat this process for each bin. Each speed range is called a bin.4/15/2015 HW10: Chap 17.7.5. and multiply that value by the fraction of molecules in that bin. take the average speed of the molecules in each "bin" (for example. the average speed of molecules in the 0200 range is 100). the best measure of the kinetic energy of the entire gas is obtained by computing the mean squared velocity. This will give you the average speed of the molecules in the gas. (v 2 ) avg . Understanding mean square velocity The mean square velocity is given by (v 2 ) avg = (∑ v 2 )/N . In contrast.7. Take the central speed value of each bin as an estimate of the speed of all the molecules in that bin.masteringphysics. Then take the square root. ANSWER: 2 (v ) avg = 2.5. The speed of sound in air must be slower than the average speed of the molecules because it is the movement of the molecules that transmits sound.6 What is the rms speed v rms of the molecules in the nitrogen gas? Express your answer numerically to three significant digits.69×105 m2 /s 2 ANSWER: v rms = 519 m/s Correct A speed of 519 m/s is comparable to that of a bullet shot from a handgun. How to approach the problem The rms speed of a system of molecules is the square root of the average of the squares of the velocities. this equation reduces to 2 (v ) avg = ∑ bins nbin v N 2 . Hint 1. where the sum is taken over all the molecules in the gas and N is the total number of molecules. Chap. Compute the weighted average squared speed.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 14/21 . a Boeing 747 jet airliner has a maximum air speed of 270 m/s and the speed of sound in air is only about 330 m/s. where the sum is now over the number of discrete bins and n bin is the number of molecules (or equivalently the percentage of molecules) in a particular bin.418. using the percentage of molecules in a bin as the weighting factor for that bin. https://session. If you take the central speed value of each bin as an estimate of the speed of all the molecules in that bin. Hint 2. Hint 1. Part C What is the temperature T of the sample of N2 gas described in the histogram? Express your answer in degrees Celsius to three significant figues.4/15/2015 HW10: Chap 17. 18. Find the mean square velocity What is the mean square velocity (v 2 ) avg for the given distribution of molecules? Express your answer numerically in meters squared per second squared to three significant figures.17. 0 g/mol ANSWER: T = 29.418.7. ANSWER: The peak moves to the right. and the formula for kinetic energy. Solve this equation for T .5.4/15/2015 HW10: Chap 17. and mm is the molar mass in kilograms. while the distribution becomes less spread out. It also lets you move a small interval around on the histogram to highlight all of the molecules within the speed range of that part of the histogram. This applet allows you to see the curves for the MaxwellBoltzmann distribution at many different temperatures.masteringphysics. Use R = 8. Hint 2. the majority of the molecules have a speed near the average speed.4 ∘ C Correct Part D The histogram used in this problem is obviously only an approximation of the true distribution of velocities in a gas. the speeds of molecules in a gas follow what is known as the MaxwellBoltzmann distribution. with a few molecules traveling very fast or very slow. while the distribution becomes more spread out. the ideal gas law. The peak moves to the right. For a given temperature. T is the temperature in kelvins. Find the molar mass of N2 To three significant figures. 18. Which of the following describes the qualitative behavior of the MaxwellBoltzmann distribution as temperature increases? You will have to press the "reset" button on the applet before you can change the temperature using the thermometer on the right side. To good approximation. while the distribution becomes more spread out. the molecules span a continuous range of velocities. ANSWER: mm = 28.6 Hint 1. In reality. where R is the ideal gas constant.314 J/(K ⋅ mol) .17. How to approach the problem Using the assumptions of kinematics. The peak moves to the left. while the distribution becomes less spread out. it can be shown − − − − − − − − that v rms = √ 3RT /mm .0 g/mol.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 15/21 . What is the molar mass mm of the N2 molecule? Express your answer in grams per mole to three significant figures. the weight of nitrogen is 14. The peak moves to the left. Chap. https://session. because ammonia is caustic. its physical and thermodynamic properties must be understood. as a source of hydrogen gas for welding.0 K if the gas is held at constant volume? The gas molecules can translate and rotate but not vibrate.17. sweat. Physically. Ammonia today can be mass produced inexpensively in chemical refineries. It can be used as a fertilizer. The thermodynamic properties describing the phases of ammonia (solid. in the production of nitric acid and sodium carbonate. liquid. as a refrigerant.masteringphysics. However. and gas) and the transitions between the phases are just as important. and in the infamous smelling salts used to revive unconscious people. ammonia is environmentally friendly in small quantities and has many applications in our economy.4/15/2015 HW10: Chap 17. 18. Chap. The relationship of these https://session. exposure to large quantities of it can cause illness and even death.5. indicating a higher average velocity.41 Part A How much heat does it take to increase the temperature of 3. Express your answer using three significant figures.418.7. and urine. To safely produce and store ammonia. usually getting released in respiration. Despite its inherent dangers. indicating that a greater percentage of molecules are traveling at a higher velocity than in the lowtemperature case.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 16/21 . ANSWER: Q = 2910 J Correct Part B What is the answer to the question in part (A) if the gas is monatomic? Express your answer using three significant figures. ANSWER: Q = 1750 J Correct Storing Ammonia Ammonia (NH3 ) is a colorless. Exercise 18.6 Correct At the higher temperatures. The peaks of the higher temperature curves are also broader. the peak of the curve shifts to the right.50 moles of a diatomic ideal gas by an amount 40. pungent gas at standard pressure and temperature. in metallugy. It is a natural metabolic byproduct. ammonia is a strong base that reacts with acids and metals. The pressure and temperature range for each of the phases is shown by its own unique area of the graph.5.418. Other points not lying on the boundary can also be used to help identify various thermodynamic processes. ANSWER: liquid. any section of curve on the diagram can be named using two letters on the boundary in alphabetical order.6 phases to pressure and temperature is quantitatively described by ammonia's pT phase diagram. Hint 1. and other quantities can be determined for any pressure. or solid. the melting temperature.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 17/21 . Express your answer as two words separated by commas in the order they appear in the sentence. Choose from the following list: gas.masteringphysics. Be careful to put the letters in the correct order. ANSWER: https://session.7. boiling temperature.17. The lines bounding each of the phases on the diagram represent the temperatures and pressures at which two states can coexist. Describe boiling in terms of phase changes Boiling is the transition from one phase to another with both phases existing together. Chap. which section of curve represents the pressure and temperature values at which ammonia will boil? Express your answer as two letters that lie on a section of the appropriate curve. the pressure axis is not to scale.gas ANSWER: boiling curve = CE Correct Part B The line between which two points would describe a process of liquid ammonia boiling completely away? Express the answer as two letters representing the endpoints of the line in order so that going from the first letter to the second letter would show a process of boiling.4/15/2015 HW10: Chap 17. 18. The phases and direction of change involved in boiling are __________ to __________. in this diagram. Note that. Part A On the phase diagram. liquid. For this problem. From the diagram. 17. which section of curve represents the pressure and temperature values at which ammonia will sublimate? Express the answer as two letters that lie on a section of the appropriate curve. Choose from the following list: gas.masteringphysics. which section of curve represents the pressure and temperature values at which ammonia https://session. ANSWER: solid.418.5. Be careful to put the letters in the correct order. or solid. 18.4/15/2015 HW10: Chap 17. Chap.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 18/21 . ANSWER: AF Correct The heat added to a substance undergoing sublimation must be equal to the heat of fusion plus the heat of vaporization.gas ANSWER: sublimation curve = BC Correct Part D The line between which two points would describe a process of sublimation for ammonia? Express your answer with two letters ordered in the direction of sublimation.7. liquid. Express your answer as two words separated by a comma in the order they appear in the sentence. Hint 1. Describe the process of sublimation The phases and direction of change for sublimation are __________ to __________.6 HG Correct Part C On the phase diagram. Part E On the phase diagram. com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 19/21 . ANSWER: melting curve = CD Correct Part F The line between which two points would describe the process of complete melting of ammonia? Express your answer as two letters ordered in the direction of melting. what is the letter name for the triple point of ammonia? Express the answer as a single letter. ANSWER: triple point = C ANSWER: T triple . liquid. Determine the letter name for the triple point Given that the triple point is the pressure and temperature at which all three phases can coexist. ptriple = 195.0. where gas. Determine the temperature to the nearest 5 K and the pressure to one significant digit.05 https://session. ANSWER: AH Correct Part G One of the most important points on a phase diagram is the triple point. 18. Chap.masteringphysics.7.17.6 will melt? Express the answer as two letters that lie on a section of the appropriate curve. Be careful to put the letters in the correct order. ptriple ) of the triple point of ammonia in the diagram? Express your answer as an ordered pair.5. Hint 1.4/15/2015 HW10: Chap 17. and solid phases all can exist at once.418. What are the coordinates ( T triple . To circumvent this problem. Chap. How to approach the problem Because the liquid and vapor forms both exist in the container. For transportation. The three phases of water will not coexist at any other temperature. but these values vary with pressure as seen in the phase diagram of ammonia. modern temperature scales are based on the triple point of water.7. Hint 1. If a container of ammonia is transported in an temperaturecontrolled truck that is maintained at no greater than 330 K . the measurement used to calibrate the temperature scale would be inaccurate. regardless of the pressure. find the point on the graph where the given temperature intersects the curve representing the phase change of liquid to gas.01∘ C at 0.5.4/15/2015 HW10: Chap 17. 18. Part A What minimum external pressure p1 must be applied to the solid if a melting phase transition is to be observed? ANSWER: p 1 = 610 Pa Correct https://session. ammonia is stored as a liquid under its own vapor pressure.3∘ C . So if one did not control and measure the pressure precisely. Part H At one atmosphere of pressure and temperatures above −33.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 20/21 . ANSWER: p = 8 atm Correct Exercise 18.49 Solid water (ice) is slowly warmed from a very low temperature. The triple point temperature of water is 0.006 atm. This means that the liquid and gas phases exist simultaneously. so the temperature can be calibrated without an additional pressure measurement. what maximum pressure p must the sides of the container be able to withstand? Express the answer numerically in atmospheres to one significant figure.6 Correct Temperature scales were originally based upon the melting and boiling points of a substance.17.418. The triple points of mercury and other substances are also used as standards for calibrating thermometers.masteringphysics. ammonia exists as a gas. 418.masteringphysics. What is this pressure? ANSWER: p2 = 2. 18.17.7. https://session. Chap.5. You received 50.6 Part B Above a certain maximum pressure p2 .8 out of a possible total of 50 points.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3545494 21/21 .4/15/2015 HW10: Chap 17.21×107 Pa Correct Score Summary: Your score on this assignment is 102%. no boiling transition is observed.