An ideal gas ( γ = 1.5 ) occupying 1 litre at 300 K and an initial pressure of 100 kPa undergoes a sudden compression to half its original volume. Calculate the work done by the gas during this process.

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Quantrex Academy · Accepted Answer

Correct answer: A. -82.8 J

The work done by the gas in an adiabatic process is given by

W = \dfrac{P_1 V_1 - P_2 V_2}{\gamma - 1}

.

The initial state is

P_1 = 10^5 \text{ Pa}

and

V_1 = 10^{-3} \text{ m}^3

, so

P_1 V_1 = 100 \text{ J}

.

The final volume is

V_2 = 0.5 \times 10^{-3} \text{ m}^3

and the final pressure is

P_2 = 2\sqrt{2} \times 10^5 \text{ Pa}

.

The product

P_2 V_2 = (2\sqrt{2} \times 10^5) \times (0.5 \times 10^{-3}) = 100\sqrt{2} \approx 141.4 \text{ J}

.

Substituting these into the work equation gives

W = \dfrac{100 - 141.4}{1.5 - 1} = \dfrac{-41.4}{0.5} = -82.8 \text{ J}

.

An ideal gas ( γ = 1.5 ) occupying 1 litre at 300 K and an initial...

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