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Graphs

Question

Suppose 0.5 mole of an ideal gas undergoes an isothermal expansion as energy is added to it as heat Q. Graph shows the final volume V_f versus Q. The temperature of the gas is
( use In 9 = 2 and R= $\large \frac{{25}}{3}J/mo{l^ - }K$ )

Moderate

A

293K
B

360K
C

386K
D

412K

Solution

From 1^st law of thermodynamics $\large Q\, = \,\Delta U\, + w$
For isothermal process, $\large \Delta U$ = 0
$\large Q\, = \,w = nRT\ln \left( {\frac{{{v_2}}}{{{v_1}}}} \right)$
$\large 1500\, = \,0.5 \times \frac{{25}}{3} \times T \times \ln \left( {\frac{{0.3}}{{0.1}}} \right)$
T = 360K

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