Question

An ideal diatomic gas occupies a volume $V_{1}$ at a pressure $P_{1}$ . The gas undergoes a process in which the pressure is proportional to the volume. At the end of process the root mean square speed of the gas molecules has doubled from its initial value then the heat supplied to the gas in the given process is

• A. $7P_{1}V_{1}$
• B. $8P_{1}V_{1}$
• C. $9P_{1}V_{1}$
• D. $10P_{1}V_{1}$

Answer 1

Answer: (C)

As $P \propto V$
$\therefore $ $PV^{- 1}=$ constant
Also, $C=C_{v}-\frac{R}{x - 1}$
$C=\frac{5}{2}R-\frac{R}{- 1 - 1}$
$C=3R$
root mean square speed is, $v=\sqrt{\frac{3 R T}{M}}$
But as root mean square speed is doubled therefore temperature becomes four times.
Hence, $\Delta Q=nC\Delta T=n\times 3R\times \left(4 T_{1} - T_{1}\right)=9nRT_{1}$
$\Delta Q=9P_{1}V_{1}$