A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $1.4$. Vessel is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by ... ( $R =$ universal gas constant )
A$\frac{ Mv ^{2}}{7 R }$
B$\frac{ Mv ^{2}}{5 R }$
C$2 \frac{ Mv ^{2}}{7 R }$
D$7 \frac{ Mv ^{2}}{5 R }$
JEE MAIN 2022, Medium
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B$\frac{ Mv ^{2}}{5 R }$
b $\frac{ C _{ P }}{ C _{ v }}=1+\frac{2}{ F }=1.4 \Rightarrow F =5$
By conservation of energy
$\frac{ F }{2} nR \Delta T =\frac{1}{2}[ nm ] v ^{2}$
$\Delta T =\frac{ mv ^{2}}{ FR }=\frac{ Mv ^{2}}{5 R }$
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