1, mole of an ideal gas at temperature T₁ expands according to law (P/V) = constant. work done whe

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11.Thermodynamics

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$1\, mole$ of an ideal gas at temperature $T_1$ expands according to the law $(P/V) =$ constant. Find the work done when the final temperature becomes $T_2$

A

$R\,\left( {{T_2} - {T_1}} \right)$

B

$(R/2)\,(T_2 -T_1)$

C

$(R/4)\,(T_2 -T_1)$

D

$PV\,(T_2 -T_1)$

Solution

$W=\int_{V_{1}}^{V_{2}} P d V=\int_{V_{1}}^{V_{2}} K V d V$

$\left(\because \frac{p}{V}=\text { constant }\right)$

$\therefore W=\frac{1}{2} k\left(V_{2}^{2}-V_{1}^{2}\right)$

$P V=R T$

But $p=K V$

$\therefore K V^{2}=R T$

or $K\left(V_{2}^{2}-V_{1}^{2}\right)=R\left(T_{2}-T_{1}\right)$

$\therefore W=\frac{R}{2}\left(T_{2}-T_{1}\right)$

Standard 11

Physics

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