An ideal gas, $\overline{\mathrm{C}}_{\mathrm{v}}=\frac{5}{2} \mathrm{R}$, is expanded adiabatically against a constant pressure of 1 atm untill it doubles in volume. If the initial temperature and pressure is $298 \mathrm{~K}$ and $5 \mathrm{~atm}$, respectively then the final temperature is _________ $\mathrm{K}$ (nearest integer).
[$\overline{\mathrm{c}}_{\mathrm{v}}$ is the molar heat capacity at constant volume]
Answer (integer)
274
Solution
<p>$-1\left(2 V_1-V_1\right)=n \times \frac{5 R}{2}\left(T_2-T_1\right)$</p>
<p>$$\begin{aligned}
& -\mathrm{V}_1=\frac{5}{2}\left(n R T_2-5 \mathrm{~V}_1\right) \\
& -\mathrm{V}_1=2.5\left(\mathrm{nRT_{2 } )}-12.5 \mathrm{~V}_1\right. \\
& 11.5 \mathrm{~V}_1=2.5\left(\mathrm{nRT_{2 } )}\right. \\
& 11.5 \times \frac{n R T_1}{P_1}=2.5 \times\left(n R T_2\right) \\
& \mathrm{T}_2=274.16 \mathrm{~k} \\
& \approx 274 \text { (Nearest integer) } \\
&
\end{aligned}$$</p>
About this question
Subject: Chemistry · Chapter: Thermodynamics · Topic: Zeroth and First Law
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