One mole of an ideal monoatomic gas is heated | vedclass

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(D) The change in internal energy $(\Delta U)$ for an ideal gas is given by the formula: $\Delta U = n C_{v} \Delta T$.For a monoatomic gas, the molar

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$1.25 	imes 10^{3} 	ext{ J}$

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(D) The change in internal energy $(\Delta U)$ for an ideal gas is given by the formula: $\Delta U = n C_{v} \Delta T$.For a monoatomic gas, the molar heat capacity at constant volume is $C_{v} = \frac{3}{2} R$.Given values:$n = 1 	ext{ mol}$$\Delta T = T_{2} - T_{1} = (100 + 273) - (0 + 273) = 100 	ext{ K}$$R = 8.32 	ext{ J mol}^{-1} 	ext{ K}^{-1}$Substituting these values into the formula:$\Delta U = 1 	imes \left( \frac{3}{2} 	imes 8.32 ight) 	imes 100$$\Delta U = 1.5 	imes 8.32 	imes 100$$\Delta U = 1248 	ext{ J}$Rounding to the nearest significant figure provided in the options, we get $\Delta U \approx 1.25 	imes 10^{3} 	ext{ J}$.

Molecule type	$\frac{C_{P}}{C_{v}}$
$A$. Monoatomic	$I$. $\frac{7}{5}$
$B$. Diatomic rigid molecules	$II$. $\frac{9}{7}$
$C$. Diatomic non-rigid molecules	$III$. $\frac{4}{3}$
$D$. Triatomic rigid molecules	$IV$. $\frac{5}{3}$

One mole of an ideal monoatomic gas is heated at a constant pressure from $0^{\circ} C$ to $100^{\circ} C$. The change in the internal energy of the gas is (Given, $R = 8.32 \text{ J mol}^{-1} \text{ K}^{-1}$):

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