Physics 535 HW: ENTROPY Name 1. In question 1, we consider processes similar to Process A from the tutorial, with a block with heat capacity 400 J/K and initial temperature 280 K and a second block with heat capacity 200 J/K and initial temperature 340 K. A. In process B, the 280 K block and 340 K block change in temperature, but in the opposite direction as in process A. In other works, the temperature of the 280 K block decreases to 260 K and the 340 K block increases to 380 K. The blocks are still thermally isolated from all other objects. 1. Is process B allowed by the first law of thermodynamics? Explain your reasoning. 2. What is the total change in entropy of the two-block system during process B? B. In process C, both blocks begin at 300 K but their temperatures diverge so that the block with heat capacity 400 J/K ends up at a temperature of 280 K and the other ends up at 340 K. (Note that this process is the reverse of process A). 1. Is process C allowed by the first law of thermodynamics? Explain your reasoning. 2. Using your result from part A.5, find the change in entropy for each block and for the two-block system during process C. C. The following questions refer to processes A (from the tutorial), B, and C. 1. For those processes that you would expect to observe, was the total change in entropy of all systems involved greater than, less than, or equal to zero? 2. For those processes that you would not expect to observe, was the total change in entropy of all systems involved greater than, less than, or equal to zero? Adapted with permission from Michael Loverude ENTROPY Physics 535 2. Consider a macroscopic system of two blocks that are in thermal contact. The two-block system is isolated from the rest of the universe. Initially, a hotter block is at a temperature TH and a colder block is at a temperature TC. In the final state of the system, the two blocks are at the same intermediate temperature TI. A. Compare the following quantities for the initial state and final state: Entropy for the block that starts at TH Sf > Si Sf < Si Si = Sf not enough information Entropy for the block that starts at TL Sf > Si Sf < Si Si = Sf not enough information Combined entropy for the two block system Sf > Si Sf < Si Si = Sf not enough information B. Consider the following statement: “When the blocks approach equilibrium, they move to a final state that is more natural, so their level of order increases.” Do you agree with this statement? Does this statement agree with the second law of thermodynamics? Adapted with permission from Michael Loverude Physics 535 ENTROPY 3. An ice cube with a mass of 30.0 g is dropped into a beaker of water. The initial temperature of the ice cube is 0° C and the initial temperature of the water in the beaker is 20° C. The heat capacity of the water in the beaker is 2000 J/K. The latent heat of fusion for water is 333 J/g. Assume that the system consisting of the beaker and the cube does not thermally interact with its surroundings. A. Determine the equilibrium temperature of the system. B. Find the changes in entropy for the following processes and carefully specify the system (or subsystem) for which you found ΔS. a. the melting of the ice cube: (Hint: Does the temperature of the ice change during this process?) b. the cooling of the water as the ice cube is melting: c. the heating of the melted ice to its final temperature: d. the cooling of the warm water to its final temperature: C. Find the total change in entropy during the process: D. Would you expect the reverse of this process (i.e., 30 g of ice forms spontaneously from a beaker of water at the final temperature) to occur? Is the reverse of this process forbidden by the first or second law of thermodynamics? Adapted with permission from Michael Loverude ENTROPY Physics 535 Consider two blocks. The initial temperature of block 1 is 280 K and the initial temperature of block 2 is 340 K. The heat capacities of blocks 1 and 2 are 400 J/K and 200 J/K, respectively. A. The two blocks are placed in thermal contact with one another but are perfectly insulated from the remainder of their surroundings. We will call the process that begins when the blocks are brought in contact with one another process A. 1. Determine the final temperature of the two blocks. 2. Determine the heat transfer to each block during process A (including sign). In lecture we articulated the relationship dS = dQ / T for an infinitesimal reversible change. Since entropy is a state function, we can calculate the change in entropy for any process by imagining reversible processes that have the same initial and final state as the process. For Process A, we can imagine placing block 1 in contact with a series of thermal reservoirs at temperatures T1, T1 + δT, T1 + 2δT, . . . Tfinal and placing block 2 in contact with a series of thermal reservoirs at temperatures T2, T1 - δT, T1 - 2δT, . . . Tfinal. Thus we replace dQ by CP dT and integrate to find the change in entropy. 3. Write an expression for ΔS by integrating dS = dQ / T, given that dQ = CP dT. 4. Determine the change in entropy during process A (including sign) • for block 1: • for block 2: 5. Is process A reversible? Explain. 1 Adapted with permission from Michael Loverude • for the system Physics 310 ENTROPY In the tutorial homework, you will consider two related processes involving this pair of blocks. Process B has the same starting point as process A, but the temperatures of the blocks diverge, so that the cold block gets colder and the hot block gets hotter. Process C is the reverse of Process A, in which two blocks start at the same temperature but one spontaneously cools and the other warms up. B. In process B, the 280 K block and 340 K block change in temperature, but in the opposite direction as in process A. In other works, the temperature of the 280 K block decreases to 260 K and the 340 K block increases to 380 K. The blocks are still thermally isolated from all other objects. 1. Is process B allowed by the first law of thermodynamics? Explain your reasoning. 2. What is the total change in entropy of the two-block system during process B? C. In process C, both blocks begin at 300 K but their temperatures diverge so that the block with heat capacity 400 J/K ends up at a temperature of 280 K and the other ends up at 340 K. (Note that this process is the reverse of process A). 1. Is process C allowed by the first law of thermodynamics? Explain your reasoning. 2. Using your result from part A.5, find the change in entropy for each block and for the two-block system during process C. D. The following questions refer to processes A, B, and C. 1. For those processes that you would expect to observe, was the total change in entropy of all systems involved greater than, less than, or equal to zero? 2. For those processes that you would not expect to observe, was the total change in entropy of all systems involved greater than, less than, or equal to zero? 2 Adapted with permission from Michael Loverude
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