5 text{moles} of an unknown gas is heated at | vedclass

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(D) $1$. Use the relation $c_p - c_v = R$. $2$. Given $c_p = 8 \ 	ext{cal/mol} \cdot ^\circ 	ext{C}$ and $R = 8.36 \ 	ext{J/mol} \cdot ^\circ 	ext

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$300$

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(D) $1$. Use the relation $c_p - c_v = R$. $2$. Given $c_p = 8 \ 	ext{cal/mol} \cdot ^\circ 	ext{C}$ and $R = 8.36 \ 	ext{J/mol} \cdot ^\circ 	ext{C}$. Since $1 \ 	ext{cal} \approx 4.18 \ 	ext{J}$, we have $R \approx 8.36 / 4.18 = 2 \ 	ext{cal/mol} \cdot ^\circ 	ext{C}$. $3$. Calculate $c_v$: $c_v = c_p - R = 8 - 2 = 6 \ 	ext{cal/mol} \cdot ^\circ 	ext{C}$. $4$. The change in internal energy $\Delta U$ for an ideal gas at constant volume is given by $\Delta U = n c_v \Delta T$. $5$. Here $n = 5 \ 	ext{moles}$, $c_v = 6 \ 	ext{cal/mol} \cdot ^\circ 	ext{C}$, and $\Delta T = 20^\circ 	ext{C} - 10^\circ 	ext{C} = 10^\circ 	ext{C}$. $6$. Therefore, $\Delta U = 5 	imes 6 	imes 10 = 300 \ 	ext{cal}$.

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