To raise the temperature of a certain mass of gas by

Question:

To raise the temperature of a certain mass of gas by $50^{\circ} \mathrm{C}$ at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by $100^{\circ} \mathrm{C}$ 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) ?

  1. 5

  2. 3

  3. 6

  4. 7


Correct Option: , 3

Solution:

$\mathrm{nC}_{p}(50)=160$

$\mathrm{nC}_{\mathrm{v}}(100)=240$

$\Rightarrow \frac{C_{p}}{2 C_{\gamma}}=\frac{160}{240}=\frac{\gamma}{2}$

$\therefore \gamma=\frac{4}{3}$ and $\mathrm{f}=\frac{2}{\gamma-1}=6$

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