2 cubic meter of diatomic gas at 6 ATM of pressure is first brought to a pressure of 2 ATM in an isovolumetric process, and then allowed to expand to a volume of 6 cubic meters. What is the work done by the gas in the process?
To find the work done by the gas in the process, we need to calculate the area under the pressure-volume curve on a thermodynamic diagram. Since the process is described as isovolumetric (constant volume) and then an expansion (change in volume), we will need to break down the calculations into two parts.
1. Isovolumetric process (constant volume):
In this process, the gas is held at a constant volume. Since the volume remains the same, the work done is zero. Therefore, no work is done during the isovolumetric process.
2. Expansion process:
The work done during the expansion process can be calculated using the formula:
Work = Pressure * Change in Volume
Given:
Initial Pressure (P1) = 6 ATM
Final Pressure (P2) = 2 ATM
Initial Volume (V1) = 2 cubic meters
Final Volume (V2) = 6 cubic meters
To find the work done during the expansion process, we need to calculate the difference in volume (ΔV) and multiply it by the average pressure during the expansion process.
ΔV = V2 - V1 = 6 - 2 = 4 cubic meters
Average pressure during the expansion process can be calculated by taking the average of the initial and final pressures:
Average Pressure = (P1 + P2) / 2 = (6 + 2) / 2 = 4 ATM
Now, we can calculate the work done:
Work = Average Pressure * ΔV = 4 ATM * 4 cubic meters = 16 ATM-cubic meters
Therefore, the work done by the gas in the process is 16 ATM-cubic meters.