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. Understand that work done by a gas is given by the formula: \( W = P \Delta V \), where \( P \) is the pressure and \( \Delta V \) is the change in volume.
2. In the first process, the volume remains constant, which means \( \Delta V = 0 \). Therefore, the work done in this process is \( W_1 = 0 \).
3. In the second process, the gas is compressed at a constant pressure of \( 5.00 \times 10^5 \) Pa from an initial volume of \( 0.200 \) m\(^3\) to a final volume of \( 0.120 \) m\(^3\). Calculate the change in volume: \( \Delta V = V_{final} - V_{initial} = 0.120 - 0.200 \) m\(^3\).
4. Substitute the values into the work formula for the second process: \( W_2 = P \Delta V = 5.00 \times 10^5 \times (0.120 - 0.200) \) m\(^3\).
5. The total work done by the gas during both processes is the sum of the work done in each process: \( W_{total} = W_1 + W_2 \). Since \( W_1 = 0 \), the total work is simply \( W_2 \).

Key Concepts

Work Done by a Gas

In thermodynamics, the work done by a gas during a process is calculated as the integral of pressure with respect to volume. For processes at constant pressure, the work done is simply the product of the pressure and the change in volume (W = PΔV). If the volume does not change, as in an isochoric process, no work is done.

Isochoric Process

An isochoric process is a thermodynamic process in which the volume remains constant. Since the volume does not change, no work is done by or on the system during this process. However, changes in pressure and temperature can occur, affecting the internal energy of the gas.

Isobaric Process

An isobaric process is a thermodynamic process that occurs at a constant pressure. During this process, the work done by the gas can be calculated using the formula W = PΔV, where P is the constant pressure and ΔV is the change in volume. This process often involves changes in both volume and temperature.