JEE Mains · Physics · STD 11 - 12 . kinetic theory of gases
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 \(7 \frac{ Mv ^{2}}{5 R }\)
Answer & Solution
Correct Answer
(B) \(\frac{ Mv ^{2}}{5 R }\)
Step-by-step Solution
Detailed explanation
\(\frac{ C _{ P }}{ C _{ v }}=1+\frac{2}{ F }=1.4 \Rightarrow F =5\) 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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