Physics Q35 – JEE-MAIN 2026

Home Physics ThermodynamicsQuestion #509

One gas of

n_{1}

mole of molecules at temperature

T_{1}

, volume

V_{1}

, and pressure

P_{1}

, and another gas of

n_{2}

mole of molecules at temperature

T_{2}

, volume

V_{2}

, and pressure

P_{2}

are mixed resulting in pressure

P

and volume

V

of the mixture. The temperature of the mixture is _______.

Clue 1 of 3: Ideal Gas Law

The behavior of ideal gases is governed by the Ideal Gas Law, which relates pressure, volume, temperature, and the number of moles.

🧠 Full Solution Path

Step 1: Express moles of each gas using the Ideal Gas Law✦ Active

For the first gas, the Ideal Gas Law states $P_{1} V_{1} = n_{1} R T_{1}$ . Therefore, the number of moles $n_{1}$ can be expressed as:

n_{1} = \frac{P_{1} V_{1}}{R T_{1}}

Similarly, for the second gas:

n_{2} = \frac{P_{2} V_{2}}{R T_{2}}

Step 2: Apply conservation of moles and Ideal Gas Law to the mixture○ Expand

When the two gases are mixed, the total number of moles $n_{t o t a l}$ is the sum of the individual moles:

n_{t o t a l} = n_{1} + n_{2}

For the mixture, the Ideal Gas Law applies as $P V = n_{t o t a l} R T_{m i x}$ , where $P$ and $V$ are the pressure and volume of the mixture, and $T_{m i x}$ is its temperature. Solving for $T_{m i x}$ :

T_{m i x} = \frac{P V}{n_{t o t a l} R} = \frac{P V}{(n_{1} + n_{2}) R}

💡 Teacher's Secret Hint

Remember that the gas constant $R$ is the same for all ideal gases.

Step 3: Substitute expressions for

n_{1}

and

n_{2}

and simplify○ Expand

Substitute the expressions for $n_{1}$ and $n_{2}$ from Step 1 into the equation for $T_{m i x}$ from Step 2:

T_{m i x} = \frac{P V}{(\frac{P_{1} V_{1}}{R T_{1}} + \frac{P_{2} V_{2}}{R T_{2}}) R}

Factor out $R$ from the denominator and simplify:

T_{m i x} = \frac{P V}{R (\frac{P_{1} V_{1}}{R T_{1}} + \frac{P_{2} V_{2}}{R T_{2}})} = \frac{P V}{(\frac{P_{1} V_{1}}{T_{1}} + \frac{P_{2} V_{2}}{T_{2}})}

Combine the terms in the denominator by finding a common denominator:

T_{m i x} = \frac{P V}{\frac{P_{1} V_{1} T_{2} + P_{2} V_{2} T_{1}}{T_{1} T_{2}}}

Invert and multiply to get the final expression for $T_{m i x}$ :

T_{m i x} = \frac{P V T_{1} T_{2}}{P_{1} V_{1} T_{2} + P_{2} V_{2} T_{1}}

This expression matches option 2.

💡 Teacher's Secret Hint

Be careful with algebraic manipulation, especially when dealing with fractions in the denominator.

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Physics Question 35 – JEE-MAIN 2026

Clue 1 of 3: Ideal Gas Law

🧠 Full Solution Path