JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Heat & Thermodynamics

A diatomic gas

(γ = 1.4)

does 400 J of work when it is expanded isobarically. The heat given to the gas in the process is ______ J.

Answer: 1400

Solution

For an isobaric (constant pressure) process, the heat supplied is:

Q = n C_{p} Δ T

Using the relation

C_{p} = \frac{γ}{γ - 1} R

and the first law:

Q = \frac{γ}{γ - 1} \cdot n R Δ T

For an isobaric process, work done

W = n R Δ T = 400

J

Therefore:

Q = \frac{γ}{γ - 1} \cdot W = \frac{1.4}{1.4 - 1} \times 400 = \frac{1.4}{0.4} \times 400 = 3.5 \times 400 = 1400

J

The heat given to the gas is 1400 J.

JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Integer answer

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