Question

As a system increases in volume, it absorbs 53.0 j of energy in the form of heat from the surroundings. the piston is working against a pressure of 0.505 atm. the final volume of the system is 59.6 l. what was the initial volume of the system if the internal energy of the system decreased by 109.7 j?

Answer 1

The first law of thermodynamics, ΔU = Q - W, and the work formula, W = -PΔV, are applied to the given values of heat absorbed, change in internal energy.

Step-by-step explanation:

To find the initial volume of a gas system where volume increases and energy is exchanged, we use the first law of thermodynamics, which connects the change in internal energy (ΔU) to heat (Q) and work (W) done by or on the system: ΔU = Q - W.

Here, Q is positive since heat is absorbed, and W is negative as work is done by the system. We can calculate W using the pressure and the change in volume, W = -PΔV, converting atm to joules by using the factor 101.325 J/L*atm.

Given that the system absorbs 53.0 J of heat, decreases in internal energy by 109.7 J, and final volume is 59.6 L, with external pressure at 0.505 atm, and W = -(0.505 atm)(ΔV)(101.325 J/L*atm), we solve for initial volume (Vi) that satisfies ΔU = Q - W with the final volume (Vf) given.