Topic: Thermodynamics
As shown in Fig. below, an ideal gas is confined to a cylinder by a piston. The piston is pushed down slowly so that the gas temperature remains at 27°C During the compression, 900 J of work is done on the gas. Find the entropy change of the gas.
- A. 3 J/K
- B. -3 J/K
- C. -6 J/K
- D. 6 J/K
Answer: B. -3 J/K
Explanation: Applying the first law of thermodynamics, $\partial Q = dU + \partial W$. Since the temperature is kept constant (isothermal compression), the change in internal energy $dU = 0$. Since 900 J of work is done *on* the gas, $\partial W = -900$ J. Thus, heat transfer $\partial Q = -900$ J. The change in entropy is $dS = \frac{\partial Q}{T}$. With $T = 27^{\circ}C = 300$ K, $dS = -\frac{900}{300} = -3$ J/K.