To raise the temperature of a certain mass of gas by 50^{\circ}C at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100^{\circ}C at constant volume,240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal ) ?
Option: 1 5
Option: 2 6
Option: 3 3
Option: 4 7

Answers (1)

\begin{array}{l} As \ \ \mathrm{Q}=\mathrm{nC}_{\mathrm{p}} \Delta \mathrm{T} \\ 160=\mathrm{nC}_{\mathrm{p}}(50)....(1) \\ 240=\mathrm{nC}_{\mathrm{v}} 100....(2) \end{array}

\frac{C_{p}}{ C_{v}}=\gamma ....(3)

So from equation (1) and (2) and (3)

we get

\frac{C_{p}}{2 C_{v}}=\frac{160}{240}=\frac{\gamma}{2}\\ \therefore \gamma=\frac{4}{3} \text { and } \mathrm{f}=\frac{2}{\gamma-1}=6

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