COMEDK · Physics · 13. Thermodynamics
If the ratio of specific heat of a gas at constant pressure to that at constant volume is \(\gamma\), the change in internal energy of a mass of a gas when the volume changes from \(\mathrm{V}\) to \(3 \mathrm{~V}\) at constant pressure is
- A \(\dfrac{2 P V}{\gamma}\)
- B \(\dfrac{R}{(\gamma-1)}\)
- C \(\dfrac{2 P V}{(\gamma-1)}\)
- D \(2 P V\)
Answer & Solution
Correct Answer
(C) \(\dfrac{2 P V}{(\gamma-1)}\)
Step-by-step Solution
Detailed explanation
The change in internal energy \(\Delta U\) for an ideal gas is given by the formula \(\Delta U = n C_{v} \Delta T\). For an ideal gas, \(C_{v} = \dfrac{R}{\gamma - 1}\). Thus, \(\Delta U = n \left( \dfrac{R}{\gamma - 1} \right) \Delta T\). Using the ideal gas law \(PV = nRT\),…
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