First Law of Thermodynamics: a Container of Ideal Gas Has

First law of thermodynamics: A container of ideal gas has a movable frictionless piston. This container is placed in a very large water bath and slowly compressed so that the temperature of the gas remains constant and equal to the temperature of the water. Which of the following statements about this gas are true for this process? (There may be more than one correct choice.)

A) Heat leaves the gas during the compression.
B) Since the gas and water are at the same temperature, no heat can flow between them, which makes this an adiabatic compression.
C) The internal (thermal) energy of the gas does not change during the compression.
D) The internal energy of the gas increases during the compression because work is done on the gas.
E) Since the temperature of the gas remains constant, the pressure of the gas must also remain constant.