2. A sample of an ideal gas underwent an expansion against a constant external pressure of 1.0 bar from 1.0 m3, 20.0 bar, and 273 K to 100.0 m3, 1.0 bar, and 273 K. What is the work done by the system on the surroundings
Isn't this impossible? The gas is ideal: PV=nRT, and T is constant so P1V1=P2V2. But that is not satisfied according to the info, so there is no isotherm that can give the work done.
To calculate the work done by the system on the surroundings during the expansion of an ideal gas, you can use the formula:
Work = Pext * ΔV
Where:
- Work is the work done by the system on the surroundings (in Joules).
- Pext is the external pressure (in Pascals) against which the gas expanded.
- ΔV is the change in volume of the gas (in cubic meters).
In this case, the external pressure is given as 1.0 bar, which is equivalent to 100,000 Pascals.
The change in volume, ΔV, can be calculated by subtracting the initial volume from the final volume:
ΔV = Vfinal - Vinitial
Given that the initial volume, Vinitial, is 1.0 m^3 and the final volume, Vfinal, is 100.0 m^3, we can substitute these values into the formula to calculate the change in volume:
ΔV = 100.0 m^3 - 1.0 m^3
ΔV = 99.0 m^3
Now, we can substitute the values of external pressure and change in volume into the formula to calculate the work done by the system on the surroundings:
Work = Pext * ΔV
Work = 100,000 Pa * 99.0 m^3
To convert the unit of pressure from Pascals to bars, we need to divide by 100,000 (since 1 bar = 100,000 Pa):
Work = (100,000 Pa * 99.0 m^3) / 100,000
Work = 99.0 J (Joules)
Therefore, the work done by the system on the surroundings during the expansion is 99.0 Joules.
To calculate the work done by the system on the surroundings during an expansion, you can use the formula:
Work Done = -Pext * ΔV
Where:
- Work Done represents the work done by the system on the surroundings.
- Pext represents the external pressure applied to the system.
- ΔV represents the change in volume of the system.
In this scenario, the initial volume (V1) is 1.0 m3, the final volume (V2) is 100.0 m3, and the external pressure (Pext) is 1.0 bar.
First, calculate the change in volume (ΔV):
ΔV = V2 - V1
= 100.0 m3 - 1.0 m3
= 99.0 m3
Next, substitute the values into the formula:
Work Done = -Pext * ΔV
= -1.0 bar * 99.0 m3
Finally, convert the unit of pressure from bar to pascals (1 bar = 100,000 Pascals) and calculate the answer:
Work Done = -1.0 bar * 99.0 m3 * 100,000 Pa/bar
= -9,900,000 Pa·m3
Therefore, the work done by the system on the surroundings is -9,900,000 Pa·m3.