The molar heat capacity for an ideal gas at c | vedclass

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(B) For an ideal gas,the relationship between molar heat capacities is $C_{p,m} - C_{v,m} = R$.Given $C_{p,m} = 20.785 \ J \ K^{-1} \ mol^{-1}$ and $R

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$2$

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(B) For an ideal gas,the relationship between molar heat capacities is $C_{p,m} - C_{v,m} = R$.Given $C_{p,m} = 20.785 \ J \ K^{-1} \ mol^{-1}$ and $R = 8.314 \ J \ K^{-1} \ mol^{-1}$,we calculate $C_{v,m}$ as:$C_{v,m} = 20.785 - 8.314 = 12.471 \ J \ K^{-1} \ mol^{-1}$.The change in internal energy $\Delta U$ is given by the formula $\Delta U = n C_{v,m} \Delta T$.Here,$\Delta U = 5000 \ J$ and $\Delta T = 500 \ K - 300 \ K = 200 \ K$.Substituting the values: $5000 = n 	imes 12.471 	imes 200$.$n = \frac{5000}{12.471 	imes 200} = \frac{25}{12.471} \approx 2.0046$.The nearest integer is $2$.

The molar heat capacity for an ideal gas at constant pressure is $20.785 \ J \ K^{-1} \ mol^{-1}$. The change in internal energy is $5000 \ J$ upon heating it from $300 \ K$ to $500 \ K$. The number of moles of the gas is [Nearest integer] (Given: $R = 8.314 \ J \ K^{-1} \ mol^{-1}$)

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