Physics Q47 – JEE-MAIN 2026

Home Physics ThermodynamicsQuestion #507

A vessel contains

0.15 m^{3}

of a gas at pressure

8 bar

and temperature

140^{\circ} C

with

c_{p} = 3 R

and

c_{v} = 2 R

. It is expanded adiabatically till pressure falls to

1 bar

. The work done during this process is _______ k J. (R is gas constant)

Enter Calculated Numerical Value:

Clue 1 of 3: Understand the Process

Identify the type of thermodynamic process (adiabatic) and recall its defining characteristics and relevant formulas.

🧠 Full Solution Path

Step 1: Calculate Adiabatic Index (

γ

) and Final Temperature (

T_{2}

)✦ Active

Given specific heats $c_{p} = 3 R$ and $c_{v} = 2 R$ . The adiabatic index is calculated as $γ = \frac{c_{p}}{c_{v}}$ . The initial temperature $T_{1}$ must be converted to Kelvin.

γ = \frac{3 R}{2 R} = 1.5

T_{1} = 140^{\circ} C + 273 = 413 K

T_{2} = T_{1} {(\frac{P_{2}}{P_{1}})}^{(γ - 1) / γ} = 413 K \times {(\frac{1 bar}{8 bar})}^{(1.5 - 1) / 1.5}

T_{2} = 413 \times {(\frac{1}{8})}^{0.5 / 1.5} = 413 \times {(\frac{1}{8})}^{1 / 3} = 413 \times \frac{1}{2} = 206.5 K

Step 2: Calculate the Number of Moles (

n

)○ Expand

Using the ideal gas law $P_{1} V_{1} = n R T_{1}$ , we can find the number of moles $n$ . Ensure all units are in SI.

n = \frac{P_{1} V_{1}}{R T_{1}} = \frac{(8 \times 10^{5} Pa) \times (0.15 m^{3})}{(8.314 {J mol}^{- 1} K^{- 1}) \times (413 K)}

n = \frac{1.2 \times 10^{5}}{3433.982} \approx 34.94 mol

Step 3: Calculate Work Done (

W

)○ Expand

The work done during an adiabatic process is given by the formula $W = \frac{n R (T_{1} - T_{2})}{γ - 1}$ . The final answer should be in kilojoules.

W = \frac{n R (T_{1} - T_{2})}{γ - 1} = \frac{34.94 mol \times 8.314 {J mol}^{- 1} K^{- 1} \times (413 K - 206.5 K)}{1.5 - 1}

W = \frac{34.94 \times 8.314 \times 206.5}{0.5} \approx 120000 J

W = 120 kJ

💡 Teacher's Secret Hint

Alternatively, one could calculate $V_{2}$ using $P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$ and then use $W = \frac{P_{1} V_{1} - P_{2} V_{2}}{γ - 1}$ .

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Physics Question 47 – JEE-MAIN 2026

Clue 1 of 3: Understand the Process

🧠 Full Solution Path