A sample of ideal gas (gamma = 1.4) is heated | vedclass

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(C) For an ideal gas at constant pressure,the heat supplied $Q$ is given by $Q = n C_p \Delta T$.The work done by the gas is $W = P \Delta V = n R \De

Vedclass · Accepted Answer

$28.57$

Vedclass · Answer

(C) For an ideal gas at constant pressure,the heat supplied $Q$ is given by $Q = n C_p \Delta T$.The work done by the gas is $W = P \Delta V = n R \Delta T$.We know that the molar heat capacity at constant pressure is $C_p = \frac{\gamma R}{\gamma - 1}$.Substituting this into the heat equation: $Q = n \left( \frac{\gamma R}{\gamma - 1} \right) \Delta T$.From the work equation,we have $n R \Delta T = W$. Substituting this into the heat equation:$Q = W \left( \frac{\gamma}{\gamma - 1} \right)$.Rearranging to solve for $W$:$W = Q \left( \frac{\gamma - 1}{\gamma} \right)$.Given $Q = 100 \ J$ and $\gamma = 1.4$:$W = 100 \left( \frac{1.4 - 1}{1.4} \right) = 100 \left( \frac{0.4}{1.4} \right) = 100 \left( \frac{4}{14} \right) = 100 \left( \frac{2}{7} \right) \approx 28.57 \ J$.

Column-$I$	Column-$II$
$(a)$ Graph $(a)$	$(i)$ Adiabatic process
$(b)$ Graph $(b)$	$(ii)$ Isobaric process
	$(iii)$ Isochoric process

$A$ sample of ideal gas $(\gamma = 1.4)$ is heated at constant pressure. If $100 \ J$ of heat is supplied to the gas,the work done by the gas is ...... $J$.

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