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  4. If the ratio of specific heat of a gas at constant pressure to that at the constant volume is γ , the change in internal energy of the mass of gas, when the volume changes from V to 2V at constant pressure p, is

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Q. If the ratio of specific heat of a gas at constant pressure to that at the constant volume is $\gamma $ , the change in internal energy of the mass of gas, when the volume changes from V to 2V at constant pressure p, is

NTA AbhyasNTA Abhyas 2020Thermodynamics

Solution:

$\quad \Delta U = n C _{ v } \Delta T$
Also, $\frac{ C _{ p }}{ C _{ v }}=\gamma$
Hence $\frac{ C _{ p }- C _{ v }}{ C _{ v }}=\gamma-1$
$\Rightarrow \quad C _{ v }= R /(\gamma-1)$
$\Delta U =\frac{ nR }{\gamma-1} \Delta T =\frac{ p \Delta V }{\gamma-1}=\frac{ p (2 V - V )}{\gamma-1}=\frac{ pV }{\gamma-1}$