Final answer:
In an isothermal process, the change in internal energy is zero, therefore the heat added to the expanding gas is equal to the work done by the gas, which is pV(ln4).
Step-by-step explanation:
In an isothermal process, the temperature of the gas remains constant. Therefore, the change in internal energy (ΔU) is zero. By the first law of thermodynamics, we have:
Q = W
where Q is the heat absorbed by the gas and W is the work done by the gas.
In this case, the gas expands quasi-statically and isothermally from a state with pressure p and volume V to a state with volume 4V. The work done by the gas is given by:
W = pV(ln4)
Since Q = W, the amount of heat added to the expanding gas is also equal to pV(ln4).