Kinetic Theory

JEE Main level, single correct, medium

95 of 168

Question 95 of 168

To raise the temperature of a certain mass of gas by 50∘C50^{\circ}C at a constant pressure,160160 calories of heat is required. When the same mass of gas is cooled by 100∘C100^{\circ}C at constant volume,240240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

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Answer: (B) 66

At constant pressure :
∆Q=nCP∆T∆Q={nC}_{P}∆T ⇒160=nCP.50\Rightarrow 160={nC}_{P}.50 .....(1)
At constant volume
∆Q=nCv∆T∆Q={nC}_{v}∆T ⇒240=nCv.100\Rightarrow 240={nC}_{v}.100......(2)
Equation (1) divided by (2)
160240=CPCV⋅50100\dfrac{160}{240}=\dfrac{{C}_{P}}{{C}_{V}}\cdot \dfrac{50}{100}
CPCV=43=1+2f\dfrac{{C}_{P}}{{C}_{V}}=\dfrac{4}{3}=1+\dfrac{2}{f}
f=6f=6

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