The internal energy of a gas is 900 J. The gas is compressed adiabatically, and its volume decreases by 100 cm3. If the pressure applied on the gas during compression is 1 atm, what is the internal energy of the gas after the adiabatic compression?
The answer is 890 J, but I don't understand why.
Ei= 900J
Ef: ?
Q= 0
Ef - Ei = Q - W
Ef= Ei - W
W= p (Vf-Vi)
P=1 atm= 10^5 Pa
This is how the answer is solved.
Ef= 900J - 10^5Pa * 100 (10^-2)^3
Ef=890J
However, since it says the volume decreases by 100 cm3 shouldn't the work be negative?
In terms of Vf-Vi the answer there should be -100cm3 not +100cm3 since the initial volume has lost 100 cm3.
Ef= 900J + 10^5Pa * 100 (10^-2)^3
Ef=910 J
This is the wrong answer that I get.
To understand why the work done on the gas is positive rather than negative in this case, we need to consider the definition of work done in thermodynamics and the direction of the change in volume.
In thermodynamics, work is defined as the product of the applied pressure and the change in volume. When a gas is compressed, the volume decreases, and the work done on the gas is positive. When a gas expands, the volume increases, and the work done by the gas is negative.
In this problem, the gas is compressed adiabatically, which means there is no heat transfer(Q=0). The volume decreases by 100 cm^3, indicating a compression. Since the pressure applied is 1 atm, we can convert it to SI units (1 atm = 10^5 Pa).
Now, let's calculate the work done on the gas during compression:
Work = pressure * change in volume
W = (10^5 Pa) * (-100 cm^3) * (10^-2 m/cm)
W = -100 J
The negative sign indicates that work is done on the gas during compression, meaning external agents are doing work on the gas to decrease its volume.
To find the final internal energy (Ef) of the gas, we can use the equation:
Ef = Ei - W
Ef = 900 J - (-100 J) = 900 J + 100 J = 1000 J
So, the correct answer is 1000 J, not 890 J. It seems there was a mistake in the given answer.