One mole of an ideal gas with gamma = 1.4 is | vedclass

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(B) The change in internal energy $\Delta U$ of an ideal gas is given by the formula $\Delta U = n C_v \Delta T$.For an ideal gas,$C_v = \frac{R}{\gam

Vedclass · Accepted Answer

$166$

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(B) The change in internal energy $\Delta U$ of an ideal gas is given by the formula $\Delta U = n C_v \Delta T$.For an ideal gas,$C_v = \frac{R}{\gamma - 1}$.Given: $n = 1 \, mol$,$\gamma = 1.4$,$R = 8.3 \, J/mol \cdot K$.Initial temperature $T_1 = 27^{\circ}C = 27 + 273 = 300 \, K$.Final temperature $T_2 = 35^{\circ}C = 35 + 273 = 308 \, K$.Change in temperature $\Delta T = T_2 - T_1 = 308 - 300 = 8 \, K$.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$.Thus,the change in internal energy is $166 \, J$.

One mole of an ideal gas with $\gamma = 1.4$ 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 ....... $J$ $(R = 8.3 \, J/mol \cdot K)$.

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