A gas undergoes two processes. In the first, the volume remains constant at 0.200 m^3 and the pressure increases from 2.00 * 10^5 Pa to 5.00 * 10^5 Pa. The second process is a compression to a volume of 0.120 m^3 at a constant pressure of 5.00 * 10^5 Pa. (b) Find the total work done by the gas during both processes.

Verified step by step guidance

1. Identify the type of processes involved. The first process is isochoric (constant volume), and the second process is isobaric (constant pressure).
2. Recall the formula for work done by a gas, which is W = P \\Delta V, where P is the pressure and \\Delta V is the change in volume. For an isochoric process, since the volume does not change, \\Delta V = 0, and thus no work is done (W = 0).
3. Calculate the change in volume for the second process. Since it is an isobaric process, use the initial and final volumes to find \\Delta V = V_{final} - V_{initial} = 0.120 m^3 - 0.200 m^3.
4. Substitute the values into the work formula for the second process. Use the constant pressure and the change in volume calculated in the previous step.
5. Add the work done in both processes to find the total work done by the gas. Since the work done in the first process is zero, the total work done is just the work done during the second process.

Key Concepts

Work Done by a Gas

In thermodynamics, the work done by a gas during expansion or compression is calculated using the formula W = PΔV, where W is work, P is pressure, and ΔV is the change in volume. If the volume remains constant, as in the first process, the work done is zero since ΔV is zero. In contrast, during compression, work is done on the gas, which is calculated using the pressure and the change in volume.

Constant Volume Process

A constant volume process, also known as an isochoric process, occurs when a gas is confined to a fixed volume, meaning that no work is done by the gas during this process. In the given question, the gas's volume remains at 0.200 m^3 while the pressure increases, indicating that the internal energy of the gas changes, but the work done is zero.

Constant Pressure Process

A constant pressure process, or isobaric process, occurs when a gas expands or compresses while maintaining a constant pressure. In the second process described, the gas is compressed to a volume of 0.120 m^3 at a constant pressure of 5.00 * 10^5 Pa. The work done during this process can be calculated by finding the difference in volume multiplied by the constant pressure, reflecting the energy transferred to or from the gas.