QuestionQuestion

1. Your backyard swimming pool contains 57,000 kg of water initially at 28°C and is out of thermal equilibrium with the air at 5 °C (the pool cover is on!). What is the maximum useable work that could be extracted from the thermal equilibration of the pool with the air? Assume that a Carnot engine could be operated between the pool and the air at a fixed temperature of 5°C.
*Note: the temperature of the pool water will change as heat is withdrawn! Use an isochoric heat capacity of Cv = 4.184 J g¹ K-¹ for the pool water and ignore any volume change of the water in the pool.

2. Calculate the change in entropy of one mole of an ideal gas for the following processes:
a. Isochoric heating from 298 K to 523 K
b. Isobaric heating from 298 K to 523 K
c. Reversible adiabatic expansion, where the initial temperature is 298 K and the final volume is twice that of the initial
d. Reversible isothermal expansion at 298 K to a final volume that is twice that of the initial
e. Free adiabatic expansion, where the initial temperature is 298 K and the final volume is twice that of the initial for an ideal gas
*Note: Assume Cv = EnR and Cp = Cv- + nR.

3. You leave a small quantity (0.021 kg) of liquid water in your Nalgene bottle on the porch outside overnight, and it gets supercooled to -30 °C (remaining as a liquid below the freezing point of water). The bottle is perfectly thermally insulated from the surroundings. When you open the lid, a snowflake (of negligible mass) falls in, and the system comes to equilibrium.
Assume that the process is adiabatic and occurs at constant atmospheric pressure (1 bar). Determine both:
a. the final state of the system (i.e., the final temperature, T2, and the molar ratio of water to ice) out of the following potential outcomes:
i. entirely ice at temperature T2
ii. entirely liquid water at T2
iii. ice water of a certain mixture at 0 °C and,
b. the change in entropy for the process.
Use the following data for water: CP(I) = 75 J mol-¹ K-¹, CP(s) = 34 J mol-¹ K-¹, and AHfus = AHmelt = 6008 J mol-¹
*Note: processes that are adiabatic and isobaric are also isenthalpic. Also, this is a highly irreversible process, but find the final state and then connect the initial and final state by a reversible path to calculate AS.

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