An ideal gas at 27 is compressed adiabatically to (8/27) of its original volume. If ratio of specific heats, γ = 5/3 then the rise in temperature of the gas is (a) 500 K (b) 125 K (c) 250 K (d) 375 K

Answer: (d). Adiabatic: T₂ = T₁((V₁)/(V₂))γ-1, T₁ = 300 K. T₂ = 300(27/8)2/3 = 300 × 9/4 = 675 K Rise = 675 - 300 = 375 K So the answer is (d) 375 K.

An ideal gas at 27 is compressed adiabatically to (8/27) of its… | MHT CET 2021 (22 Sep, Shift 2)

Q185MHT CET 2021 · 22 SEP · SHIFT 2Medium

Thermodynamic Processes

An ideal gas at $27^\circ\text{C}$ is compressed adiabatically to $(8/27)$ of its original volume. If ratio of specific heats, $\gamma = 5/3$ then the rise in temperature of the gas is

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Answer: (d)

Adiabatic: $T_2 = T_1\left(\frac{V_1}{V_2}\right)^{\gamma-1}$ , $T_1 = 300\ \text{K}$ .
$T_2 = 300\left(\frac{27}{8}\right)^{2/3} = 300 \times \frac{9}{4} = 675\ \text{K}$
Rise $= 675 - 300 = 375\ \text{K}$
So the answer is (d) 375 K.

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