A balloon filled with air increases its volume to 58.0 L

Question

A balloon filled with air increases its volume to 58.0 L against a constant external pressure of 0.963 atm and in the process, 107.6 J of energy is absorbed in the form of heat from the surroundings. Calculate the initial volume of the system if the internal energy of the system decreases by 352.7 J during the process.

Answer 1

work (w) = - pressure (P) x change in volume (∆V)

Change in internal energy (∆U) = heat (Q) + work (w)

Q = +107.6 J

∆U = -352.7 J

w = ?

Soving for w:

-352.7 J = 107.6 J + w

w = -460.3 J (negative meaning system is doing work on the surroundings)

Use w = -P∆V to find the initial volume:

-460.3 J = -(0.963 atm)(∆V)

recall that 1 L-atm = 101.325 J

-460.3 J x 1 L-atm / 101.325 J = -4.54 L-atm

-4.54 L-atm = -(0.963 atm) (∆V)

∆V = 4.7 L

Initial volume = 58.0 L - 4.7 L = 53.3 L

Be sure to check the math