Question 137 of 190

Starting at temperature $300K,$ one mole of an ideal diatomic gas $\left(\gamma =1.4\right)$ is first compressed adiabatically from volume ${V}_{1}$ to ${V}_{2}=\dfrac{{V}_{1}}{16}.$ It is then allowed to expand isobarically to volume $2{V}_{2}$ . If all the processes are the quasi-static then the final temperature of the gas (in ${}^{o}K$ ) is (to the nearest integer) ___________.

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Answer: 1819

$P{V}^{y}=constant$
$T{V}^{-1}=constant$
$300{\left({V}_{1}\right)}^{1.4-1}={T}_{B}{\left(\dfrac{{V}_{1}}{16}\right)}^{2/5}$
${T}_{B}=300\times {2}^{8/5}$
Now for BC process
$\dfrac{{V}_{B}}{{T}_{B}}=\dfrac{{V}_{c}}{{T}_{c}}$
${T}_{c}=\dfrac{{V}_{c}{T}_{B}}{{v}_{B}}=2\times 300\times {2}^{8/5}$
${T}_{c}=1818.859$
${T}_{c}=1819K$