Logo
Jeeify
NVAEasyJEE 2026First Law & Internal Energy

JEE Physics 2026 Question with Solution

A diatomic gas (γ=1.4\gamma = 1.4) does 100 J100 \, \text{J} of work when it is expanded isobarically. Then the heat given to the gas is _____ J\text{J}.

Answer

Correct answer:350

Step-by-step solution

Standard Method

Given: A diatomic gas has γ=1.4\gamma = 1.4 and does work W=100 JW = 100 \, \text{J} during an isobaric expansion.

Find: The heat given to the gas, QQ.

In an isobaric process,

W=PΔV=nRΔTW = P\Delta V = nR\Delta T

and the heat supplied is

Q=nCpΔTQ = nC_p\Delta T

Using

Cp=γRγ−1C_p = \frac{\gamma R}{\gamma - 1}

we get

Q=n(γRγ−1)ΔTQ = n \left( \frac{\gamma R}{\gamma - 1} \right) \Delta T Q=γγ−1(nRΔT)Q = \frac{\gamma}{\gamma - 1}(nR\Delta T)

Since nRΔT=WnR\Delta T = W,

Q=γγ−1WQ = \frac{\gamma}{\gamma - 1} W

Substitute γ=1.4\gamma = 1.4 and W=100 JW = 100 \, \text{J}:

Q=1.41.4−1×100Q = \frac{1.4}{1.4 - 1} \times 100 Q=1.40.4×100Q = \frac{1.4}{0.4} \times 100 Q=3.5×100=350 JQ = 3.5 \times 100 = 350 \, \text{J}

Therefore, the heat given to the gas is 350 J350 \, \text{J}.

Using the heat-work ratio

Given: The process is isobaric and the gas has γ=1.4\gamma = 1.4.

Find: Heat supplied QQ.

For any isobaric process,

QW=CpR=γγ−1\frac{Q}{W} = \frac{C_p}{R} = \frac{\gamma}{\gamma - 1}

For γ=1.4\gamma = 1.4,

QW=1.40.4=3.5\frac{Q}{W} = \frac{1.4}{0.4} = 3.5

Hence,

Q=3.5×100=350 JQ = 3.5 \times 100 = 350 \, \text{J}

Therefore, the required heat is 350 J350 \, \text{J}.

Common mistakes

  • Using Q=WQ = W for an isobaric process. This is wrong because part of the heat increases the internal energy and the rest appears as work. Use Q=nCpΔTQ = nC_p\Delta T and W=nRΔTW = nR\Delta T instead.

  • Using γ−1γ\frac{\gamma - 1}{\gamma} instead of γγ−1\frac{\gamma}{\gamma - 1}. This inverts the required ratio and gives a much smaller answer. Start from Cp=γRγ−1C_p = \frac{\gamma R}{\gamma - 1} carefully.

  • Substituting γ=1.4\gamma = 1.4 incorrectly as 1.41.4\frac{1.4}{1.4} or taking 1.4−1=1.01.4 - 1 = 1.0. This is wrong arithmetic. The correct subtraction is 1.4−1=0.41.4 - 1 = 0.4.

Practice more First Law & Internal Energy questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step — free to start.

Start free trialMore on First Law & Internal Energy

Related questions