Question

As a system increases in volume, it absorbs 51.0 J of energy in the form of heat from the surroundings. The piston is working against a pressure of 0.557 atm. The final volume of the system is 55.1 L. What was the initial volume of the system if the internal energy of the system decreased by 104.7 J

Answer 1

Answer:

V₁ = 57.9 L.

Explanation:

The initial volume can be found by calculating the work done on the system:

$W = -P(V_{2} - V_{1})$

Where:

P: is the pressure = 0.557 atm

V₂: is the final volume = 55.1 L

V₁: is the initial volume =?

Now, the work can be calculated as follows:

$\Delta E = Q + W$

Where:

ΔE: is the internal energy of the system = -104.7 J

Q: is the heat absorbed = 51.0 J  

$W = \Delta E - Q = -104.7 J - 51.0 J = -155.7 J$

Hence, the initial volume is:

$V_{1} = V_{2} - \frac{W}{P} = 55.1 L - \frac{-155.7 J*\frac{1 atm*L}{101.34 J}}{0.557 atm} = 57.9 L$                  

Therefore, the initial volume of the system is 57.9 L.

I hope it helps you!