A sample of gas is compressed from 12.93 L to 3.83 L using a constant external pressure of 4.89 atm. At the same time, 1,957 J of heat flows into the surroundings. What is the internal energy change for the gas?
First the work part.
work = -p(V2-V1) = -4.89(3.83 - 12.93) = + ?
? x 101.325 = + work in joules.
Then U = Q + W
Q is 1,957 J flowing TO THE surroundings so Q will be -1,957 J.
Plug all of that into the above and solve.
Post your work if you get stuck.
To find the internal energy change for the gas, you can use the equation:
ΔU = q - PΔV
where:
- ΔU is the change in internal energy
- q is the heat flow
- P is the external pressure
- ΔV is the change in volume
In this case, you are given:
- q = 1,957 J (heat flow)
- P = 4.89 atm (external pressure)
- ΔV = V2 - V1 = 3.83 L - 12.93 L = -9.1 L
Note that the change in volume is negative since the gas is being compressed.
Now, we need to convert the units of external pressure and volume to SI units (Joules and meters cubed) because the units need to be consistent:
1 atm = 101325 Pa (Pascals)
1 L = 0.001 m^3 (cubic meters)
Converting the external pressure:
4.89 atm * 101325 Pa/atm = 496650.525 Pa
Converting the change in volume:
-9.1 L * 0.001 m^3/L = -0.0091 m^3
Now, we can substitute the values into the equation:
ΔU = 1,957 J - (496650.525 Pa * -0.0091 m^3)
Simplifying the equation:
ΔU = 1,957 J - (-4526.615075 J)
= 1,957 J + 4526.615075 J
= 6483.615075 J
Therefore, the internal energy change for the gas is approximately 6483.615075 J.