Two identical samples of a monatomic gas are initially at pressure P and occupy volume V. You perform two experiments which will both lead to the gas samples being compressed to final volumes one-third as large as their initial volumes. In one of the experiments you make the gas undergo an isothermal compression. In the second you make the gas undergo an adiabatic compression. It is correct to say that:
A) The isothermal compression leads to a higher final pressure than the adiabatic compression and the gas exchanges heat with its surroundings.
B) The adiabatic compression leads to a higher final pressure than the isothermal compression and the gas does not exchange heat with its surroundings.
C) The isothermal compression leads to a lower final pressure than the isothermal compression and the gas does not exchange heat with its surroundings.
D) The adiabatic compression leads to a lower final pressure than the isothermal compression and the gas exchanges heat with its surroundings.
E) It is impossible to predict on the basis of this data.

Question

Quizplus · Accepted Answer

During an isothermal compression, the temperature remains constant, so the ideal gas law can be used to find that the pressure has to increase to maintain the constant temperature. However, in an adiabatic compression, no heat is exchanged with the system's surroundings. Therefore, the energy must be conserved. During an adiabatic compression, the internal energy must increase, and thus the pressure must increase to maintain the constant temperature. Therefore, the adiabatic compression will lead to a higher final pressure than the isothermal compression.

Two Identical Samples of a Monatomic Gas Are Initially at Pressure