A triatomic molecule can have a linear conguration, as does CO2 (Figure a), or it can be nonlinear; like H20 (Figure b). Suppose the temperature of a gas of triatomic molecules is sufficiently low that vibrational motion is negligible. (1 B 0 My; [3 (a (a) What is the molar specic heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are linear? EintT = %R J (b) What is the molar specific heat at constant volume, expressed as a multiple of the universal gas constant (R) if the molecules are nonlinear? EintT = 3R J At high temperatures, a triatomic molecule has two modes of vibration, and each contributes %R to the molar specic heat for its kinetic energy and another %R for its potential energy. (c) Identify the high-temperature molar specific heat at constant volume for a triatomic ideal gas of the linear molecules. (Use the following as necessary: R.) 9 EintT = ER J (d) Identify the high-temperature molar specific heat at constant volume for a triatomic ideal gas of the nonlinear molecules. (Use the following as necessary: R.) 9 EintT = 5R A cylinder made of copper with a mass of 0.80 kg is heated to 800C, then dropped into 6.00 kg of water at 11C. What is the total change in entropy (in J/K) of the cylinder-water system, assuming no energy is lost by heat from this system to the surroundings? The specific heat of copper is 387 J/(kg - K), and the specic heat of water is 4,186 J/(kg - K). (Hint: note that d0 = mch.) _x First, consider conservation of energy. Using the specific heats, can you find the final equilibrium temperature of the combined system? Next consider the infinitesimal change in entropy d5. How does it depend on dQ and temperature? Note the expression given for dQ in the hint. Can you write an infinitesimal expression for each object that can be integrated from the initial to final temperature? J/K As shown in the figure, a cylinder with a moveable piston and containing a monatomic ideal gas in an initial state A undergoes an isovolumetric, then an isothermal, and finally an isobaric process to complete the cycle. I' (mml I} \\'(I.l (B When the gas is in the initial state, the volume is 3.00 L, the pressure is 1.00 atm, and the temperature is 300 K. The gas is first warmed at constant volume to a pressure of 2 times the initial value (state B). The gas is then allowed to expand isothermally to some new volume (state C). Finally it is compressed isobarically to its initial state. (Due to the nature of this problem, do not use rounded intermediate values in your calculationsincluding answers submitted in WebAssign.) (a) Find the number of moles of the gas. 121.87 x Check the units for your expression for the number of moles of the gas. Did you remember to convert the units for volume from L to ma? moles (b) Find the temperature of the gas at state 3 (in K). 600 K (c) Find the temperature of the gas at state C (in K). 600 \\/ K (d) Find the volume of the gas at state C (in L). 6.00 w L (e) Determine values (in kJ) for Q, W, and AEint for the process A > B. o=_x What can you say about the work done on the gas for an isovolumetric process? How does the change in internal energy depend on the change in temperature? Knowing the change in internal energy and the work done on the gas, we can use the first law of thermodynamics to determine the heat transferred. kJ W=Cw w Aer-x What can you say about the work done on the gas for an isovolumetric process? How does the change in internal energy depend on the change in temperature? Knowing the change in ini-mnal anarnu and Han \":an1 :4an An Han nac urn ran \"an Han (imp Ian: nf Fknrmndunamire m Ant-Arming the heap haneimmri In (e) Determine values (in kJ) for Q, W, and AE Q: AEint H (f) Determine values (in kJ) for Q, W, and AE Q: ll AEint (9) Determine values (in kJ) for Q, W, and AE Q: int _ (h) Determine values (in kJ) for Q, W, and AE Q: 455.95 H int for the process A > B. X What can you say about the work done on the gas for an isovolumetric process? How does the change in internal energy depend on the change in temperature? Knowing the change in internal energy and the work done on the gas, we can use the first law of thermodynamics to determine the heat transferred. kJ 455.95 ykJ X What can you say about the work done on the gas for an isovolumetric process? How does the change in internal energy depend on the change in temperature? Knowing the change in internal energy and the work done on the gas, we can use the first law of thermodynamics to determine the heat transferred. kJ 6.914 6.914 0 759.92 303.97 455.95 int for the process B > C. X What can you say about the change in internal energy for an isothermal process? How can you determine the work done on the gas for an isothermal process? Knowing the change in internal energy and the work done on the gas, we can use the first law of thermodynamics to determine the heat transferred. kJ X What can you say about the change in internal energy for an isothermal process? How can you determine the work done on the gas for an isothermal process? Knowing the change in internal energy and the work done on the gas, we can use the first law of thermodynamics to determine the heat transferred. kJ ykJ int for the process C > A. X How does the change in internal energy depend on the change in temperature? How can you determine the work done on the gas for an isobaric process? Knowing the change in internal energy and the work done on the gas, we can use the first law of thermodynamics to determine the heat transferred. k) X Check the units for your expression for the number of moles of the gas. Did you remember to convert the units for volume from L to m3? kJ X How does the change in internal energy depend on the change in temperature? Howe can you determine the work done on the gas for an isobaric process? Knowing the change in internal energy and the work done on the gas, we can use the first law of thermodynamics to determine the heat transferred. kJ int for the complete cycle A > B > C > A. x If the gas undergoes a complete cycle, and initial and final states are identical, what can we say about the change in internal energy for the cycle? Knowing the work done on the gas and the heat transfer for each process of the cycle, how can we determine these quantities for the complete cycle? How can you use the first law of thermodynamics to check your work? k] -x If the gas undergoes a complete cycle, and initial and final states are identical, what can we say about the change in internal energy for the cycle? Knowing the work done on the gas (h) Determine values (in kJ) for Q, W, and AEint for the complete cycle A > B > C > A. Q = 297.056 x If the gas undergoes a complete cycle, and initial and final states are identical, what can we say about the change in internal energy for the cycle? Knowing the work done on the gas and the heat transfer for each process of the cycle, how can we determine these quantities for the complete cycle? How can you use the rst law of thermodynamics to check your work? kJ W = 297.056 x If the gas undergoes a complete cycle, and initial and final states are identical, what can we say about the change in internal energy for the cycle? Knowing the work done on the gas and the heat transfer for each process of the cycle, how can we determine these quantities for the complete cycle? How can you use the first law of thermodynamics to check your work? kJ AEint= 0 J U Need Help? |___