A certain gas expands in volume from 1.75 L to 8.32 L at constant temperature.
Calculate the work done (in Joules) by the gas if it expands against a constant
pressure of 3.8 atm.
Please explain and show the work and correct answers.
To calculate the work done by the gas, we can use the formula:
Work = -P * ΔV
where P is the pressure, ΔV is the change in volume, and the negative sign indicates that work is done against the external pressure.
Given:
Initial volume (V1) = 1.75 L
Final volume (V2) = 8.32 L
Pressure (P) = 3.8 atm
First, we need to find the change in volume (ΔV):
ΔV = V2 - V1
= 8.32 L - 1.75 L
= 6.57 L
Now we can calculate the work using the formula:
Work = -P * ΔV
= -(3.8 atm) * (6.57 L)
To convert atm to Joules, we need to use the conversion factor:
1 atm = 101.325 J/L
Therefore, the final equation for work becomes:
Work = -(3.8 atm) * (6.57 L) * (101.325 J/L)
Calculating the value:
Work = -(-2563.389 J)
= 2563.389 J
So, the work done by the gas is approximately 2563.389 Joules.
Please note that in this calculation, we used the assumption that the gas behaves ideally (follows ideal gas laws) and that the temperature remains constant. If this is not the case, the calculations may vary.