An ideal gas occupies a volume of $2 \mathrm{~m}^{3}$ at a pressure of $3 \times 10^{6} \mathrm{~Pa}$. The energy of the gas is:

(A) $9 \times 10^{6} \mathrm{~J}$

(B) $6 \times 10^{4} \mathrm{~J}$

(D) $3 \times 10^{2} \mathrm{~J}$

JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Heat & Thermodynamics

An ideal gas occupies a volume of

2 m^{3}

at a pressure of

3 \times 1 0^{6} Pa

. The energy of the gas is:

(A) $9 \times 1 0^{6} J$ ✓ Correct
(B) $6 \times 1 0^{4} J$
(C) $1 0^{8} J$
(D) $3 \times 1 0^{2} J$

Answer: (A)

Solution

The internal (translational) energy of an ideal gas is

U = \frac{f}{2} n R T = \frac{f}{2} P V

. Taking the gas as monatomic (

f = 3

, i.e. the translational energy):

U = \frac{3}{2} P V = \frac{3}{2} (3 \times 1 0^{6}) (2) = 9 \times 1 0^{6} J

JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Single correct option

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