Sep 19, 2017

# ONE KG OF HOT WATER AT A TEMPERATURE OF 350 K (T W,0 ) IS KEPT IN AN ADIABATIC ROOM THAT CONTAINS…

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One kg of hot water at a temperature of 350 K (TW,0) is kept in an adiabatic room that contains 0.4 kg of air at a temperature of 290 K (TA,0). A Carnot engine is used to cool the water, lift a weight, and reject heat to the room air until the water and air temperatures equilibrate (cf. Figure 3.41). During the equilibration process:

a. How does the internal energy of the composite system change?

b. How does the entropy of the water change?

c. How does the entropy of the room air change?

d. How does the entropy of the composite system change?

e. Assuming water temperatures to be 340 K, 339.5 K, … K, calculate TA such that dSW + dSA = 0.

f. Determine the initial internal energy of the composite system and plot the internal energy as a function of air temperature as the water cools.

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