As a system increases in volume, it absorbs 52.5 J of energy in the form of heat from the surroundings. The piston is working against a pressure of 0.500 atm. The final volume of the system is 58.0 L. What was the initial volume of the system if the internal energy of the system decreased by 103.1 J?

54.9 L

To determine the initial volume of the system, we need to use the concept of the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat absorbed by the system minus the work done by the system:

ΔU = Q - W

Where:
ΔU is the change in internal energy
Q is the heat absorbed by the system
W is the work done by the system

Given that the internal energy of the system decreased by 103.1 J and the system absorbed 52.5 J of energy in the form of heat, we can substitute the known values into the equation:

-103.1 J = 52.5 J - W

Simplifying the equation, we have:

-103.1 J - 52.5 J = -W

-155.6 J = -W

Since the work done by the system is given by the pressure-volume work, we can use the formula:

W = -PΔV

Where:
W is the work done by the system
P is the pressure
ΔV is the change in volume

Substituting the given pressure of 0.500 atm and the final volume of 58.0 L, we have:

-155.6 J = -(0.500 atm)(58.0 L - V)

Simplifying the equation, we get:

-155.6 J = -29 atm·L + 0.500 atm·V

To isolate the initial volume, rearrange the equation:

-0.500 atm·V = -155.6 J + 29 atm·L

Divide both sides by -0.500 atm:

V = (-155.6 J + 29 atm·L) / (-0.500 atm)

Calculating the expression on the right side, we can find the initial volume of the system.