Entropy: Example Problems

Try to solve these problems before watching the solutions in the screencasts.

Example Problem 1

An ideal gas undergoes an irreversible process from 200°C and 1 bar to 110°C and 10 bar. What is the entropy change for one mole of gas?  
 CP = 30 J/mol K

Example Problem 2

An inventor has proposed to build a device that she calls a Hilsch tube to continuously create cold and hot air from a high pressure air stream at room temperature. She claims that she can feed air at 25°C and 10 bar into this device, and obtain cold air (0°C, 1 bar) and hot air (40°C, 1 bar). The device has no energy input, no moving parts, and loses no heat to the surroundings. Is this possible? If so, what fraction of the fed air can be converted to the cold air at 0°C?

Try to explain why the statements below are true.

  • A molecule has a higher entropy in the gas phase than in the liquid phase.
  • A molecule has a higher entropy in the liquid phase than in the solid phase.
  • When two components are mixed, the entropy increases.
  • When a gas phase occupies more volume at the same temperature, it has a higher entropy.
  • When temperature increases for a gas, liquid or solid at constant pressure, its entropy increases.
  • When heat transfers from a hot body to a cold body, the total entropy increases.