SATHEE: Thermodynamics Question 237

Thermodynamics Question 237

Question: An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume $V_{1}$ and contains ideal gas at pressure $P_{1}$ , and temperature $T_{1}$ The other chamber has volume $V_{2}$ and contains ideal gas at pressure $P_{2}$ and temperature $T_{2}$ If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be

Options:

A) $\frac{T_{1} T_{2} (P_{1} V_{1} + P_{2} V_{2})}{P_{1} V_{1} + P_{2} V_{2}}$

B) $\frac{P_{1} V_{1} T_{1} + P_{2} V_{2} T_{2}}{P_{1} V_{1} + P_{2} V_{2}}$

C) $\frac{P_{1} V_{1} T_{2} + P_{2} V_{2} T_{1}}{P_{1} V_{1} + P_{2} V_{2}}$

D) $\frac{T_{1} T_{2} (P_{1} V_{1} + P_{2} V_{2})}{P_{1} V_{1} T_{1} + P_{2} V_{2} T_{2}}$

Show Answer

Answer:

Correct Answer: A

Solution:

[a] Here $Q = 0$ and $W = 0.$

Therefore from first law of thermodynamics $Δ U = Q + W = 0$

$∴$ Internal energy of the system with partition = Internal energy of the system without partition. $n_{1} C_{v} T_{1} + n_{2} C_{v} T_{2} = (n_{1} + n_{2}) C_{v} T$

$∴ T = \frac{n_{1} T_{1} + n_{2} T_{2}}{n_{1} + n_{2}}$

$But n_{1} = \frac{P_{1} V_{1}}{R T_{1}} and n_{2} = \frac{P_{2} V_{2}}{R T_{2}}$

$∴ T = \frac{\frac{P_{1} V_{1}}{R T_{1}} \times T_{1} + \frac{P_{2} V_{2}}{R T_{2}} \times T_{2}}{\frac{P_{1} V_{1}}{R T_{1}} + \frac{P_{2} V_{2}}{R T_{2}}} = \frac{T_{1} T_{2} (P_{1} V_{1} + P_{2} V_{2})}{P_{1} V_{1} T_{2} + P_{2} V_{2} T_{1}}$

Thermodynamics Question 237

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Thermodynamics Question 237

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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