Final answer:
The gas's thermal energy increases by 500 J, under the assumption that all of the heat supplied is used for the work done by the gas during its expansion at constant pressure.
Step-by-step explanation:
A student asked: During a process, 500 J of heat energy is transferred to a gas.
The gas expands at constant pressure from 400 cm3 to 800 cm3. During this process, the gas's thermal energy increases by how much?
To answer this, we can use the first law of thermodynamics, which is given by the equation 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.
If 500 J of heat is supplied to the gas (Q = 500 J) and the gas expands at constant pressure doing work on its surroundings, we need to calculate the work done (W).
The work done by the gas during an isobaric (constant pressure) expansion is equal to the product of the pressure and the volume change. However, since the pressure value is not given in the question, we will assume the pressure inside the cylinder is constant and only consider the heat applied and the work done.
Here, the entire 500 J is assumed to be translated into work done by the gas since we cannot account for any heat losses or gains without additional information.
Therefore, we can assume that the gas's thermal energy increases by the full amount of heat supplied, which is 500 J. This is under the assumption that there are no other forms of energy transfer such as heat loss to the surroundings other than the work done by the gas.