JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Heat & Thermodynamics

One mole of an ideal gas at

2 7^{\circ} C

is taken from A to B as shown in the given PV indicator diagram. The work done by the system will be ____

\times 1 0^{- 1} J

.
[Given : R = 8.3J/mole K,

ℓ n2 = 0.6931

] (Round off to the nearest integer)

Answer: 17258

Solution

The gas is carried along the isotherm at

T = 2 7^{\circ} C = 300

K, and the indicator diagram shows the volume doubling from

V

2 V

. For an isothermal change one mole does work

W = n R T ln \frac{V _{f}}{V _{i}} = 1 \times 8.3 \times 300 \times ln 2 = 2490 \times 0.6931 = 1725.8

J. The blank is asked in units of

1 0^{- 1}

J, and since

1725.8

= 17258 \times 1 0^{- 1}

J, the required number is

17258

JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Integer answer

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