Thermodynamics

JEE Main level, numerical answer, medium

82 of 190

Question 82 of 190

An ideal gas initially at 0∘C0^{\circ} \mathrm{C} temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is 3/23 / 2, the change in temperature due to the thermodynamic process is _____ K.

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Answer: 273

γ=32Tvγ−1=C273 V00.5=T(V04)0.5 T=273×2=546Δ T=273\begin{aligned} & \gamma=\frac{3}{2} \\ & \mathrm{Tv}^{\gamma-1}=\mathrm{C} \\ & 273 \mathrm{~V}_0^{0.5}=\mathrm{T}\left(\frac{\mathrm{V}_0}{4}\right)^{0.5} \\ & \mathrm{~T}=273 \times 2=546 \\ & \Delta \mathrm{~T}=273\end{aligned}

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