Occupying 100 cc , an ideal gas is initially at a pressure of 2.5 × 10^5 Pa and a temperature of 300 K . It is adiabatically compressed to half its original volume. Determine the final pressure of the gas. Take γ = 1.5 .

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Quantrex Academy · Accepted Answer

Correct answer: C. 7.1 × 10^5 Pa

For an adiabatic process, the relation between pressure and volume is given by

P_1 V_1^{\gamma} = P_2 V_2^{\gamma}

.

Rearranging for the final pressure

P_2

:

P_2 = P_1 \left( \dfrac{V_1}{V_2} \right)^{\gamma}

Given

P_1 = 2.5 \times 10^5 \text{ Pa}

,

V_1 = 100 \text{ cc}

,

V_2 = 50 \text{ cc}

, and

\gamma = 1.5

:

P_2 = 2.5 \times 10^5 \times \left( \dfrac{100}{50} \right)^{1.5}

P_2 = 2.5 \times 10^5 \times (2)^{1.5}

P_2 = 2.5 \times 10^5 \times 2\sqrt{2}

Using

\sqrt{2} \approx 1.414

:

P_2 = 2.5 \times 10^5 \times 2.828

P_2 \approx 7.07 \times 10^5 \text{ Pa} \approx 7.1 \times 10^5 \text{ Pa}

Occupying 100 cc , an ideal gas is initially at a pressure of 2.5 ×...

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