First slide

Thermodynamic processes

Question

1 mole of gas expands isothermally at 37° C. The amount of heat absorbed by it until its volume doubled is (R = 8.31 mol^-1 K^-1)

Moderate

A

$411 .25 cal$
B

$418 .50 cal$
C

$420 .25 cal$
D

$425.24 cal$

Solution

Here, $T = 37^{\circ} C = 37 + 273 = 310 K, V_{2} = 2 V_{1}$
Work done in isothermal process is
$W = nRTln \frac{V_{2}}{V_{1}} = 1 \times 8 .31 \times 310 \times \ln \frac{2 V_{1}}{V_{1}}$
$= 8 .31 \times 310 \times \ln 2 = 1 .786 \times 10^{3}$ J
Amount of heat absorbed $= \frac{1 .786 \times 10^{3}}{4 .2} cal = 425.24 cal$

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