A gas is compressed from an initial volume of 5.40 L to a final volume of 1.20 L by an external pressure of 1.00 atm. During the compression the gas releases 128 J of heat. Part A What is the change in internal energy of the gas?

296.2J

Explanation:

From the first law, you should know that the change in internal energy of a system is given by:

ΔE = q + w

where q is the heat added to the system (q is negative if heat is released from the system)

and w is the work done on the system by the surroundings.

We are told that q = - 128 J.

Because the volume of the system decreases, the surroundings are doing work on the system, so w will be positive. If the compression is done "quasistatically", so that the internal pressure of the system is always infinitesimally close to the external pressure, then the work done is w = p*ΔV

1 atm = 1.01*10^5 Pa, and 1 liter = 10^-3 m^3, so:

w = (1.01^10^5 N/m^2) * (5.40 - 1.20) * 10^-3 m^3

w = 424.2 J

The change internal energy is then:

ΔE = - 128 J + 424.2J = + 296.2 J