1 mole of rigid diatomic gas performs a work of Q/5 when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is xR/8. The value of x is _________. [R = universal gas constant] Numerical answer type. Work it out, then open the answer.

Answer: 25. W = Q/5 ⇒ Δ U = 4Q/5, so Q = 5/4Δ U. C = 5/4Cv, and rigid diatomic Cv = 5/2R. C = 5/4 × 5/2R = 25R/8 So x = 25.

1 mole of rigid diatomic gas performs a work of Q/5 when heat Q is… | JEE Main 2021 (26 Feb, Shift 2)

Q196JEE Main 2021 · 26 FEB · SHIFT 2Medium

Thermodynamic Processes

1 mole of rigid diatomic gas performs a work of $\frac{Q}{5}$ when heat Q is supplied to it. The molar heat capacity of the gas during this transformation is $\frac{xR}{8}$ . The value of x is _________. [R = universal gas constant]

Numerical answer type. Work it out, then open the answer.

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Answer: 25

$W = \frac{Q}{5} \Rightarrow \Delta U = \frac{4Q}{5}$ , so $Q = \frac{5}{4}\Delta U$ .
$C = \frac{5}{4}C_v$ , and rigid diatomic $C_v = \frac{5}{2}R$ .
$C = \frac{5}{4} \times \frac{5}{2}R = \frac{25R}{8}$
So $x = 25$ .

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