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 103.3 J?
To find the initial volume of the system, we can use the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system:
ΔU = Q - W
Where:
ΔU is the change in internal energy
Q is the heat added to the system
W is the work done by the system
In this case, we are given that the change in internal energy is -103.3 J, which means the internal energy of the system decreased. The heat added to the system, Q, is 52.5 J. We need to find the work done by the system, W.
To find the work done by the system, we can use the equation:
W = -PΔV
Where:
W is the work done by the system
P is the pressure
ΔV is the change in volume
In this case, the pressure, P, is given as 0.500 atm, and the change in volume, ΔV, is the final volume minus the initial volume:
ΔV = Vf - Vi
Where:
Vf is the final volume
Vi is the initial volume
We are given that the final volume, Vf, is 58.0 L. We need to find the initial volume, Vi.
Substituting the given values into the equations, we have:
-103.3 J = 52.5 J - (-0.500 atm) * (58.0 L - Vi)
Simplifying the equation:
-103.3 J = 52.5 J + 0.500 atm * (Vi - 58.0 L)
-103.3 J = 52.5 J + 0.500 atm * Vi - 29.0 atm L
Rearranging the equation:
Vi = (-103.3 J - 52.5 J + 29.0 atm L) / 0.500 atm
Vi = (-103.3 J + 29.0 atm L + 52.5 J) / 0.500 atm
Vi = (-103.3 J + 52.5 J + 29.0 atm L) / 0.500 atm
Vi = -21.8 J + 29.0 atm L / 0.500 atm
Vi = 7.2 J + 58.0 L
Vi = 65.2 L
Therefore, the initial volume of the system is 65.2 L.