A monoatomic ideal gas expands at constant pr | vedclass

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Question

(D) For an ideal gas,the heat supplied at constant pressure is given by $\Delta Q = n C_p \Delta T$.The change in internal energy is given by $\Delta

Vedclass · Accepted Answer

$0.4$

Vedclass · Answer

(D) For an ideal gas,the heat supplied at constant pressure is given by $\Delta Q = n C_p \Delta T$.The change in internal energy is given by $\Delta U = n C_v \Delta T$.According to the first law of thermodynamics,$\Delta Q = \Delta U + \Delta W$,so the work done is $\Delta W = \Delta Q - \Delta U$.Substituting the expressions,$\Delta W = n C_p \Delta T - n C_v \Delta T = n(C_p - C_v) \Delta T = n R \Delta T$.The fraction of heat used as work is $\frac{\Delta W}{\Delta Q} = \frac{n R \Delta T}{n C_p \Delta T} = \frac{R}{C_p}$.For a monoatomic gas,$C_p = \frac{5}{2} R$.Therefore,the fraction is $\frac{R}{\frac{5}{2} R} = \frac{2}{5} = 0.4$.

$A$ monoatomic ideal gas expands at constant pressure,with heat $Q$ supplied. The fraction of $Q$ which goes as work done by the gas is

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