The change in internal energy of a given mass | vedclass

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(B) The change in internal energy $\Delta U$ of an ideal gas is given by the formula $\Delta U = n C_v \Delta T$.We know that $C_v = \frac{R}{\gamma-1

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$\frac{2 PV}{\gamma-1}$

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(B) The change in internal energy $\Delta U$ of an ideal gas is given by the formula $\Delta U = n C_v \Delta T$.We know that $C_v = \frac{R}{\gamma-1}$.Substituting this,we get $\Delta U = n \left( \frac{R}{\gamma-1} \right) \Delta T = \frac{n R \Delta T}{\gamma-1}$.From the ideal gas equation at constant pressure,$PV = nRT$,so $n R \Delta T = P \Delta V$.Here,the change in volume is $\Delta V = 3V - V = 2V$.Therefore,$n R \Delta T = P(2V) = 2PV$.Substituting this into the internal energy equation: $\Delta U = \frac{2PV}{\gamma-1}$.

The change in internal energy of a given mass of a gas,when its volume changes from $V$ to $3V$ at constant pressure $P$,is (where $\gamma$ is the ratio of the specific heat capacities of the gas).

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