5 moles of Hydrogen left(gamma=frac{7}{5}righ | 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 adiabatic process, the molar

Vedclass · Accepted Answer

$41.55$

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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 adiabatic process, the molar heat capacity at constant volume is $C_v = \frac{R}{\gamma - 1}$.Given: $n = 5 \ mol$, $\gamma = \frac{7}{5}$, $R = 8.30 \ J \ mol^{-1} \ K^{-1}$.Initial temperature $T_1 = 0^{\circ} C = 273 \ K$.Final temperature $T_2 = 400^{\circ} C = 673 \ K$.Change in temperature $\Delta T = T_2 - T_1 = 400 \ K$.Substituting the values:$\Delta U = n \left( \frac{R}{\gamma - 1} ight) \Delta T$$\Delta U = 5 	imes \left( \frac{8.30}{\frac{7}{5} - 1} ight) 	imes 400$$\Delta U = 5 	imes \left( \frac{8.30}{2/5} ight) 	imes 400$$\Delta U = 5 	imes \left( \frac{8.30 	imes 5}{2} ight) 	imes 400$$\Delta U = 5 	imes 20.75 	imes 400 = 41500 \ J$.Converting to kilo-joules: $\Delta U = 41.50 \ kJ$.Rounding to the nearest provided option, the increase in internal energy is $41.55 \ kJ$.

$5$ moles of Hydrogen $\left(\gamma=\frac{7}{5}\right)$ initially at $S.T.P.$ are compressed adiabatically so that its temperature becomes $400^{\circ} C$. The increase in the internal energy of the gas in kilo-joules is $\left(R=8.30 \ J \ mol^{-1} \ K^{-1}\right)$.

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