JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Heat & Thermodynamics

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A gas mixture consists of 3 moles of oxygen and 5 moles or argon at temperature T . Considering only translational and rotational modes, the total internal energy of the system is:

(A)15 RT✓ Correct
(B)12 RT
(C)4 RT
(D)20 RT

Answer: (A)

Solution

Count the active degrees of freedom. Oxygen is diatomic, so with translation and rotation it has

f = 5

and energy

\frac{5}{2} n R T

: for

3

moles that is

\frac{5}{2} \times 3 R T = \frac{15}{2} R T

. Argon is monatomic with

f = 3

, giving

\frac{3}{2} n R T

: for

5

moles that is

\frac{3}{2} \times 5 R T = \frac{15}{2} R T

. The total internal energy is

\frac{15}{2} R T + \frac{15}{2} R T = 15 R T

JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Single correct option

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