### Thermodynamics - Questions on Entropy

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1. Calculate the change in entropy when 10 kg of air is heated at constant volume from a pressure of 101325 N/m2 and a temperature of 20oC to a pressure of 405300 N/m2. CV = 20.934 kJ/kmol.oC.
2. Calculate the total change in entropy for the following processes:
1. One gram mole of an ideal gas (CP = 7 cal/gmol.oK) is cooled at 10 atmosphere absolute pressure from 500 K to 300 K, and then expanded isothermally to 1 atmosphere absolute pressure and 300 K.
2. 100 grams of lead shot (CP = 0.03 cal/gm.oC) originally at 300oC is mixed with 100 grams of water at 30oC.

3. One kg of air is heated reversibly from an initial state of 1 atm and 10oC to 1 atm and 65oC. For reversible heating of air at constant pressure, dQ/dT = 0.24 kcal/kg.oC. Determine the change in entropy.
4. A heat engine receives 500 BTU of heat per cycle from a reservoir at 540oF and rejects heat to a sink in a hypothetical amounts of (a) 375 BTU per cycle (b) 250 BTU per cycle and (c) 150 BTU per cycle. Which of these respective cases represent a reversible cycle, an irreversible cycle and an impossible cycle?
5. What is the change in entropy when one gram mole of an ideal gas at 21oC and a pressure of 10 kgf/cm2 expands through a throttle valve to a pressure of 1 kgf/cm2. The value of the gas constant R = 1.987 cal/gmol.oK
6. A lump of copper having a mass of 10 gm at a temperature of 500oC is just dropped into a well insulated bucket containing 100 gm of water at a temperature of 50oC. If the heat capacities of copper and water are 0.095 and 1.0 respectively, expressed as cal/gm.oC, calculate the total change in entropy resulting from the process.
7. One gram mole of a perfect gas with CP = 7 cal/gmol.oK is to be expanded from 10 atm and 500 K to 1 atm and 300 K by two reversible paths.
1. Cool at 10 atm from 500 K to 300 K and expand isothermally to 1 atm at 300 K.
2. Expand at 500 K to the final volume and cool at constant volume to 300 K.

What is the change in entropy for the gas over each path? Derive the equations used.

8. A heat exchanger uses 5000 kg/hr of water to cool a hydrocarbon oil from 140oC to 65oC. The oil , flowing at the rate of 2500 kg/hr has an average specific heat of 0.6 kcal/kg.oC. The water enters at 20oC. Determine
1. The entropy change of the oil
2. Entropy change of water
3. The total entropy change as a result of this heat exchange process.

9. 15 kg of air at 200oC and 10 kgf/cm2 is cooled to 0oC and a volume of 1.2 m3. Determine the change in entropy.
10. 2 kg of oxygen execute an internally reversible process whereby heat is received causing the total entropy to increase to 0.3833 kcal/oC. For an initial temperature of 94oC, determine the final temperature, if the process is (a) constant volume (b) constant pressure. For oxygen, CP = 0.1572 kcal/kg.oC; CV = 0.2193 kcal/kg.oC.
11. A 50 kg hot steel ball at 100oC (CP = 0.02 cal/gm.oC) is cooled in atmospheric air at 25oC. Find total entropy change.
12. 1 kg (Molecular weight = 16)of an ideal gas at 25oC, 1 atm is mixed with 2 kg (Molecular weight = 40) of another ideal gas at 100oC and 30 atm. What is the total entropy change. Assume CP = 20 kJ/kmol.oK.
13. Calculate the enthalpy, entropy and molal heat capacity at constant volume (CV) of 1 gmol of nitrogen at 527oC and 100 atmosphere absolute pressure, assuming it to be an ideal gas.
Data:
CP in cal/gmol.oC = 6.5 + 0.001 T, where the temperature T is in oK.
Enthalpy is zero at 0oC, and 1 atmosphere absolute pressure.
Enthalpy is 45.8 cal/gmol.oK at 25oC and 1 atmosphere absolute pressure.

© M.Subramanian, Lecturer, Chemical Engg, SVCE, Sriperumbudur - 602105, Tamil Nadu, INDIA