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 an ideal gas is given by the formula $\Delta U = n C_v \Delta T$.For an ideal gas,$C_v = \frac{R}{\ga

Vedclass · Accepted Answer

$166$

Vedclass · Answer

(B) 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,$C_v = \frac{R}{\gamma - 1}$.Given: $n = 1 \, mol$,$\gamma = 1.4$,$R = 8.3 \, J/mol/K$,$T_1 = 27\,^{\circ}C = 300 \, K$,$T_2 = 35\,^{\circ}C = 308 \, K$.$\Delta T = T_2 - T_1 = 308 - 300 = 8 \, K$.Substituting the values:$\Delta U = 1 	imes \frac{8.3}{1.4 - 1} 	imes 8$$\Delta U = \frac{8.3}{0.4} 	imes 8$$\Delta U = 8.3 	imes 20 = 166 \, J$.

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

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