JEE Mains · Physics · STD 11 - 12 . kinetic theory of gases
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) \(?\)
- A \(5\)
- B \(3\)
- C \(6\)
- D \(7\)
Answer & Solution
Correct Answer
(C) \(6\)
Step-by-step Solution
Detailed explanation
\(nC _{ P }(50)=160\) \(nC _{ v }(100)=240\) \(\Rightarrow \frac{ C _{ p }}{2 C _{ v }}=\frac{160}{240}=\frac{\gamma}{2}\) \(\therefore \gamma=\frac{4}{3}\) and \(f =\frac{2}{\gamma-1}=6\)
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