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Q Joules of Heat is given to a sample of Helium in such a manner that the pressure remains constant throughout. The work done by the gas is then?

(A) $\large\frac{Q}{5}$ (B) $\large\frac{2Q}{5}$ (C) $\large\frac{3Q}{5}$ (D) $\large\frac{5}{Q}$

1 Answer

Since the heat is supplied at constant pressure, $ Q = nC_p \Delta T \rightarrow \Delta T = \large\frac{\Delta q}{nC_p} $$ = \large\frac{Q}{nC_p}$
Therefore, $\Delta u = nC_v \Delta T = \large\frac{Q}{C_p}$$C_v$
$\Rightarrow \Delta w = \Delta q - \Delta u = Q - Q \large\frac{C_v}{C_p}$
Since Helium is a monoatomic gas, $\large\frac{C_p}{C_v} = \large\frac{5}{2}$$R$.
$\Rightarrow \Delta w = Q \large\frac{R}{\frac{5R}{2}} $$=\large\frac{2}{5}$$Q$.
answered Mar 11, 2014 by balaji.thirumalai

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