In ideal gas of 27 is compressed adiabatically to (8/27) of its original volume. If γ = 5/3, the rise in temperature of a gas is (a) 300 K (b) 375 K (c) 400 K (d) 450 K

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

In ideal gas of 27 is compressed adiabatically to (8/27) of its… | MHT CET 2024 (16 May, Shift 1)

Q115MHT CET 2024 · 16 MAY · SHIFT 1Medium

Thermodynamic Processes

In ideal gas of $27^\circ\text{C}$ is compressed adiabatically to $(8/27)$ of its original volume. If $\gamma = \frac{5}{3}$ , the rise in temperature of a gas is

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Answer: (b)

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

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