Kinetic Theory

JEE Main level, single correct, medium

102 of 168

Question 102 of 168

When heat QQ is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by ∆T∆T . The heat required to produce the same change in temperature, at a constant pressure is:

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Answer: (B) 75Q\dfrac{7}{5}Q

For diatomic gas CP=72R{C}_{P}=\dfrac{7}{2}R
CV=52R{C}_{V}=\dfrac{5}{2}R
Heat supplied at constant volume Q=nCVΔTQ=n{C}_{V}\Delta T
Heat supplied at constant pressure Q′=nCPΔT{Q}^{'}=n{C}_{P}\Delta T
QQ′=CVCP\dfrac{Q}{{Q}^{'}}=\dfrac{{C}_{V}}{{C}_{P}}
Q′=QCPCV=75Q{Q}^{'}=Q\dfrac{{C}_{P}}{{C}_{V}}=\dfrac{7}{5}Q

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