The Coffee Cup Cooler · AI Generator #GEN-A7EFFFF5

Physics · thermodynamics

Problem

A clever engineer designs a passive cooling device for hot beverages. The device consists of a small sealed chamber containing

n = 2.5 \times 10^{-3}\;\text{mol}

of an ideal gas at initial temperature

T_i = 300\;\text{K}

and pressure

P_i = 1.0\;\text{atm}

. The chamber has a movable piston connected to a thermal reservoir at

T_c = 280\;\text{K}

. When the hot coffee cup (at

T_h = 360\;\text{K}

) is placed in contact with the chamber, the device operates as a heat engine between the coffee and the cold reservoir. The gas undergoes a complete Carnot cycle, extracting heat from the coffee and rejecting heat to the cold reservoir. During the isothermal expansion at the hot temperature, the gas volume doubles from its initial value. Calculate the net work done by the gas during one complete Carnot cycle. Use

R = 8.314\;\text{J/(mol·K)}

and assume the coffee temperature remains constant during the process.

Related theory

thermodynamics

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