Five moles of hydrogen initially at STP is co | vedclass

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(C) The change in internal energy $\Delta U$ for an ideal gas in an adiabatic process is given by the formula:$\Delta U = n C_v \Delta T$Since $C_v =

Vedclass · Accepted Answer

$41.50$

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(C) The change in internal energy $\Delta U$ for an ideal gas in an adiabatic process is given by the formula:$\Delta U = n C_v \Delta T$Since $C_v = \frac{R}{\gamma - 1}$, we have:$\Delta U = n \frac{R}{\gamma - 1} (T_2 - T_1)$Given values:$n = 5 \, mol$$T_1 = 273 \, K$ (at $STP$)$T_2 = 673 \, K$$R = 8.3 \, J/mol-K$$\gamma = 1.4$Substituting these values into the equation:$\Delta U = 5 	imes \frac{8.3}{1.4 - 1} 	imes (673 - 273)$$\Delta U = 5 	imes \frac{8.3}{0.4} 	imes 400$$\Delta U = 5 	imes 8.3 	imes 1000$$\Delta U = 41500 \, J$Converting to kilo joules:$\Delta U = 41.50 \, kJ$

Five moles of hydrogen initially at $STP$ is compressed adiabatically so that its temperature becomes $673 \, K$. The increase in internal energy of the gas, in kilo joule is $(R=8.3 \, J/mol-K; \gamma=1.4$ for diatomic gas$)$

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