Question

In the isothermal compression of a gas, the volume occupied by the gas is decreasing, but the temperature of the gas remains constant. In order for this to happen, a) heat must enter the gas. b) heat must exit the gas. c) no heat exchange should take place between the gas and the surroundings.

Short answer

Answer: b) heat must exit the gas.

Step-by-step solution

General understanding of isothermal process

For an isothermal process, the temperature of the gas remains constant. This means that the internal energy of the gas does not change, as internal energy is directly related to the temperature. Additionally, during an isothermal compression, the volume of the gas decreases. This means work must be done on the gas.

Understanding heat exchange

Since the internal energy of the gas does not change, but work is being done on the gas, this means that the energy provided to the gas in the form of work must be balanced out. This can only happen through heat exchange with the surroundings.

Determining the direction of heat exchange

For an isothermal compression process, heat must exit the gas in order to balance out the work done on it and maintain its internal energy. When work is done on the gas, energy is given to the gas, which could increase its internal energy if it is not removed. The heat must exit the gas in order to keep the temperature constant.

Conclusion

Based on the analysis and understanding of isothermal compression and heat exchange, the correct answer is: b) heat must exit the gas.