JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Chemical Thermodynamics

The molar heat capacity for an ideal gas at constant pressure is

20.785 J K^{- 1} mol^{- 1}

. The change in internal energy is 5000 J upon heating it from 300 K to 500 K . The number of moles of the gas at constant volume is

____

[Nearest integer]
(Given:

R = 8.314 J K^{- 1} mol^{- 1}

)

Answer: 2

Solution

For an ideal gas:

C_{p, m} = C_{v, m} + R

C_{v, m} = 20.785 - 8.314 = 12.471 J K^{- 1} mol^{- 1}

The change in internal energy is:

Δ U = n C_{v, m} Δ T

Given:

Solving for n:

n = \frac{Δ U}{C _{v, m} Δ T} = \frac{5000}{12.471 \times 200} = \frac{5000}{2494.2} \approx 2.00

Therefore, the answer is 2.

JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Integer answer