Calculate the work done if a gas is compressed from 8.3 L to 3.3 L at constant temperature by a constant pressure of 3.0 atm, and give your answer in units of joules. (1 L · atm = 101.3 J)
To calculate the work done when a gas is compressed, we can use the formula:
Work (W) = -P(V2 - V1)
Where:
W - work done by the gas
P - pressure
V2 - final volume
V1 - initial volume
In this case, the initial volume V1 is 8.3 L, the final volume V2 is 3.3 L, and the pressure P is 3.0 atm.
Substituting these values into the formula, we get:
W = -(3.0 atm)(3.3 L - 8.3 L)
First, let's calculate the difference in volumes:
3.3 L - 8.3 L = -5 L
Now, substitute this back into the equation:
W = -(3.0 atm)(-5 L) = 15 atm L
To convert from atm L to joules, we need to use the conversion factor: 1 L · atm = 101.3 J.
Therefore, multiply the work by the conversion factor:
W = 15 atm L × 101.3 J / L · atm = 1519.5 J
So, the work done by the gas when it is compressed from 8.3 L to 3.3 L at constant pressure of 3.0 atm is 1519.5 joules.