Final answer:
The change in the internal energy of the gas during a quasi-static isothermal expansion is 0 J, and the heat absorbed by the gas is 250 J to keep its internal energy constant.
Step-by-step explanation:
Understanding the First Law of Thermodynamics in a Quasi-static Process
According to the first law of thermodynamics, the change in the internal energy of a gas is equal to the heat added to the system minus the work done by the system. In a quasi-static and isothermal expansion, the temperature remains constant, implying that the internal energy of an ideal gas also remains constant. This is because the internal energy of an ideal gas depends only on temperature. Therefore, the change in internal energy for this process is 0 J.
Given that the gas does 250 J of work, and since there's no change in internal energy, the amount of heat absorbed by the gas must be equal to the work done by the gas to keep the internal energy constant. So, the heat absorbed by the gas is 250 J. This is in accordance with the first law of thermodynamics which can be formulated as ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.