You’ve just landed your first job at the US Patent Office in the Mechanical Systems Division. On your first day, your boss gives you a patent to evaluate. After reading the claim, you have determined that the working fluid is air and the system is closed. Also, the air changes state from 300 °C and 2.5 bar to 100 °C and 1 bar, and this change produces 3000 Joules of work per mole of air. Finally, the system rejects heat to a reservoir operating at room temperature (23 C). If one assumes that air is an ideal gas [Cp = (7/2)R] here, does the information provided above give you any basis for rejecting this patent? Please prove, either way. (Hint: Think in terms of a certain “Law” of thermodynamics that could shed light on the feasibility of this process.)
You’ve just landed your first job at the US Patent Office in the Mechanical Systems Division. On your first day, your boss gives you a patent to evaluate. After reading the claim, you have determined that the working fluid is air and the system is closed. Also, the air changes state from 300 °C and 2.5 bar to 100 °C and 1 bar, and this change produces 3000 Joules of work per mole of air. Finally, the system rejects heat to a reservoir operating at room temperature (23 C). If one assumes that air is an ideal gas [Cp = (7/2)R] here, does the information provided above give you any basis for rejecting this patent? Please prove, either way. (Hint: Think in terms of a certain “Law” of thermodynamics that could shed light on the feasibility of this process.)
Calculate the change in entropy of the air treated as an ideal gas:
For 1 mole of air:
Calculate the change in entropy of the surroundings (heat reservoir):
Where T_res=296 K (23 C) and Q_res is obtained from the closed system energy balance of the system:
Determine whether the 2nd law of thermodynamics holds where the change in entropy of the universe must be positive in order for the process to be feasible:
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