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 lJ IKl 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 nally an isobaric process to complete the cycle. I' luun) { \\ ll.) 69 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. H 0.12 / moles (b) Find the temperature of the gas at state B (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 J L H (e) Determine values (in U) for Q, W, and AEint for the process A > B. o=w W=Eix w for the process B > C. (f) Determine values (in U) for Q, W, and AEint (f) Determine values (in kJ) for Q, W, and AE Q = 7.021 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 w = 7.021 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 AEint 0 y k] int for the process B ) C. (9) Determine values (in kJ) for Q, W, and AEint for the process C > A. Q = 0.767 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 rst law of thermodynamics to determine the heat transferred. k] w = 0304 y k] 0.463 x To determine the change in internal energy AE final temperatures kJ AEint int' you need the change in temperature AT. How did you determine the change in temperature? You may have interchanged the initial and (h) Determine values (in kJ) for Q, W, and AE Q = 6.717 x f 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] w = 6.717 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 int 0 J '0 int for the complete cycle A > B > C > A. l> m H