Thermodynamics

JEE Main level, single correct, medium

169 of 190

Question 169 of 190

An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes 32 times of its initial value. If the final pressure of gas is 128 atmospheres, the value of ' γ\gamma 'of the gas is :

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Answer: (B) 1.41.4

Volume of the gas v=md\mathrm{v}=\frac{\mathrm{m}}{\mathrm{d}} and using PVγ=\mathrm{PV}^\gamma= constant
P′P=VV′=(d′d)γ or 128=(32)γ∴γ=75=1.4\begin{aligned} & \frac{\mathrm{P}^{\prime}}{\mathrm{P}}=\frac{\mathrm{V}}{\mathrm{V}^{\prime}}=\left(\frac{\mathrm{d}^{\prime}}{\mathrm{d}}\right)^\gamma \\ & \text { or } 128=(32)^\gamma \\ & \therefore \gamma=\frac{7}{5}=1.4 \end{aligned}

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