Question

Two thermally insulated identical vessels A and B are connected through a stopcock. A contains a gas at STP and B is completely evacuated. If the stopcock is suddenly opened then

• A. temperature is halved
• B. internal energy of the gas is halved
• C. internal energy of the gas and pressure are halved
• D. temperature and internal energy of the gas remain the same
• E. pressure and internal energy of the gas remain the same

Answer 1

Answer: (E)

We are given two thermally insulated identical vessels A and B, connected through a stopcock. Vessel A contains a gas at STP (Standard Temperature and Pressure), and vessel B is completely evacuated. When the stopcock is suddenly opened, the gas expands into vessel B. We need to analyze what happens to the temperature, pressure, and internal energy of the gas.

In this situation, the key concepts to consider are:

• Thermally Insulated System: No heat is exchanged with the surroundings, so the total energy of the system remains constant.
• Expansion into Vacuum (Free Expansion): The gas expands without doing any work (as vessel B is evacuated) and without heat exchange.

In free expansion of an ideal gas:

• The temperature remains constant.
• The internal energy remains constant, as it depends only on temperature for an ideal gas.
• The pressure decreases, because the gas now occupies a larger volume (both vessels A and B).

Therefore, the internal energy remains the same, but the pressure decreases.

Correct Answer:

Correct Answer: (E) internal energy remains the same