One mole of an ideal gas (gamma = 1.4) is adi | vedclass

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(B) The change in internal energy $(\Delta U)$ for $n$ moles of an ideal gas is given by the formula $\Delta U = n C_v \Delta T$.For $1$ mole of an id

Vedclass · Accepted Answer

$166$

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(B) The change in internal energy $(\Delta U)$ for $n$ moles of an ideal gas is given by the formula $\Delta U = n C_v \Delta T$.For $1$ mole of an ideal gas,$n = 1$.The molar heat capacity at constant volume is given by $C_v = \frac{R}{\gamma - 1}$.Given $\gamma = 1.4$ and $R = 8.3\,J/mol\cdot K$,we have:$C_v = \frac{8.3}{1.4 - 1} = \frac{8.3}{0.4} = 20.75\,J/mol\cdot K$.The change in temperature is $\Delta T = 35\,^oC - 27\,^oC = 8\,K$.Therefore,the change in internal energy is $\Delta U = 1 	imes 20.75 	imes 8 = 166\,J$.

One mole of an ideal gas $(\gamma = 1.4)$ is adiabatically compressed so that its temperature rises from $27\,^oC$ to $35\,^oC$. The change in the internal energy of the gas is .... $J$. (Given $R = 8.3\,J/mol\cdot K$)

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