Thermodynamics

JEE Main level, numerical answer, medium

46 of 190

Question 46 of 190

11 mole of rigid diatomic gas performs a work of Q5\dfrac{Q}{5} when heat QQ is supplied to it. The molar heat capacity of the gas during this transformation is xR8.\dfrac{xR}{8}. The value of xx is
[RR universal gas constant]

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Answer: 25

Q=ΔU+WQ=\Delta U+W
Q=ΔU+Q5Q=\Delta U+\dfrac{Q}{5}
ΔU=4Q5\Delta U=\dfrac{4Q}{5}
nCvΔT=45nCΔTn{C}_{v}\Delta T=\dfrac{4}{5}nC\Delta T
C=258RC=\dfrac{25}{8}R
x=25x=25

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