A gas at normal temperature is suddenly compressed to one-fourth of its original volume. If (Cp)/(Cv) = γ = 1.5, then the increase in its temperature is (a) 273 K (b) 373 K (c) 473 K (d) 573 K

Answer: (a). Sudden compression is adiabatic: T₂ = T₁((V₁)/(V₂))γ-1, T₁ = 273 K. T₂ = 273 × 40.5 = 546 K Increase = 546 - 273 = 273 K So the answer is (a) 273 K.

A gas at normal temperature is suddenly compressed to one-fourth of… | MHT CET 2023 (12 May, Shift 1)

Q148MHT CET 2023 · 12 MAY · SHIFT 1Medium

Thermodynamic Processes

A gas at normal temperature is suddenly compressed to one-fourth of its original volume. If $\frac{C_p}{C_v} = \gamma = 1.5$ , then the increase in its temperature is

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Answer: (a)

Sudden compression is adiabatic: $T_2 = T_1\left(\frac{V_1}{V_2}\right)^{\gamma-1}$ , $T_1 = 273\ \text{K}$ .
$T_2 = 273 \times 4^{0.5} = 546\ \text{K}$
Increase $= 546 - 273 = 273\ \text{K}$
So the answer is (a) 273 K.

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