Question

24. Suppose that an ideal gas is inside a container with a movable piston. Which of the following statements is true? 1) Increasing the temperature of the system while keeping the volume constant causes the gas to perform work. 2) When work is done by the system on the surroundings while temperature is kept constant, the pressure of the gas increases. 3) If temperature is kept constant, then decreasing the pressure of the gas causes a increase in volume 4) The gas performs work if its volume decreases and its pressure increases.

Answer 1

The statement (3) is true, i.e. If temperature is kept constant, then decreasing the pressure of the gas causes a increase in volume: this means that the process is isothermal, and it is very normal if the pressure of the gas is decreased then the volume will definitely increase, as pressure is inversely proportional to the volume of an ideal gas.

1^st statement is wrong because if volume is constant then work done will be zero, as dW = -pdV, V=constant, then dV = 0

4^th statement: if the volume is decreased and pressure is increased then the gas does not performs work instead work is done on the gaseous system.

2^nd statement: when work is done by the system then the work done is -ve, and if the temperature is constant, then there is no way that pressure of the gas will increase, as when work is being done by the system the energy of the system is decreasing, whereas on the other hand pressure increases when the energy of the system is increasing or vice versa, thus these two statements are contradicting each other so this is wrong.