Final answer:
Gas expansion work is negative when the gas does work against external pressure, signifying an energy transfer from the system to the surroundings, while work is positive during gas compression indicating work done on the system. The amount of work done is calculated by the formula w = -Pext ∆V, and during an isothermal expansion, a gas must absorb heat to do work and maintain a constant temperature.
Step-by-step explanation:
Understanding Gas Expansion Work
When discussing gas expansion work, respect for the first law of thermodynamics is essential. It indicates that when a gas expands, it performs pressure-volume work (PV work) against the external pressure, resulting in a transfer of energy from the system to the surroundings. This means that the gas does negative work because it loses energy.
Conversely, when a gas is compressed and its volume decreases, the work done on the gas is considered positive. This is because the surroundings are working on the system, thereby increasing the system's internal energy. The formula for calculating the work done during a gas expansion or compression is w = -Pext ∆V, where ∆V is the volume change and Pext is the external pressure.
It's crucial to note that during an isothermal expansion, a gas needs to absorb heat to maintain its temperature constant, because as it does work on the surroundings, its internal energy would decrease without this heat absorption. If, for example, 500 J of work are done by the gas during an expansion, and its internal energy increases by 80 J, this means the gas would have absorbed 580 J of heat in total; the energy added to the system as heat and the energy used to do work both contribute to the change in internal energy.