91Ó°ÊÓ

When discussing the work done by a gas during an isobaric process, we are referring to the amount of energy transferred by the gas as it expands at constant pressure. The key formula to remember here is:

• \( W = P \times \Delta V \)
• Where:
• \( W \) is the work done by the gas
• \( P \) is the pressure
• \( \Delta V \) is the change in volume

In our particular problem, the gas does work totaling 480 J. The pressure remains constant at \(1.6 \times 10^{5} \text{ Pa} \), highlighting the isobaric nature of the process. It's important to understand this relationship as it illustrates how pressure and volume changes translate to work being done. If there is a change in volume and the pressure stays the same, energy is being transferred either into or out of the system.

The change in volume is a crucial part of understanding the isobaric process in thermodynamics. In this scenario, we are given the initial volume and need to calculate the change in volume, \( \Delta V \), during the gas expansion.

Knowing the work done by the gas (480 J) and the constant pressure (\(1.6 \times 10^{5} \text{ Pa} \)), we use the formula \( W = P \times \Delta V \) to find \( \Delta V \):

• Rearranging gives us: \( \Delta V = \frac{W}{P} \)
• Substituting the known values: \( \Delta V = \frac{480}{1.6 \times 10^{5}} \)
• Calculating \( \Delta V \): \( \Delta V = 3 \times 10^{-3} \mathrm{m}^{3} \)

This means the volume of the gas increases by \( 3 \times 10^{-3} \mathrm{m}^{3} \) due to the work performed by the gas while expanding against constant pressure. Understanding the change in volume helps you visualize how the initial and final state of the gas relates under constant pressure.

Determining the final volume of the gas after expansion is straightforward once you know the initial volume and the change in volume. In this exercise, the initial volume of the gas is given as \( 1.5 \times 10^{-3} \mathrm{m}^{3} \). With the change in volume known from previous steps, calculating the final volume involves a simple addition:

• Use the equation: \( V_f = V_i + \Delta V \)
• Substitute into it: \( V_f = 1.5 \times 10^{-3} \text{ m}^3 + 3 \times 10^{-3} \text{ m}^3 \)
• Performing the addition gives us: \( V_f = 4.5 \times 10^{-3} \text{ m}^3 \)

This calculation clearly shows that the gas expanded to reach a final volume of \( 4.5 \times 10^{-3} \text{ m}^3 \). In real-life applications, understanding how to reach this final volume through calculations helps in examining the efficiency and effectiveness of a thermodynamic process.