One mole of an ideal gas does 3000 J of work

Question

1. One mole of an ideal gas does 3000 J of work on its surroundings as it expands isothermally to a final pressure of 1 atm and volume of 25 L. Determine

(a) the initial volume and

(b) the temperature of the gas

Answer 1

25 Liters = 0.025 Cubic Meters.

1 Atmosphere = 101325 Newtons Per Square Meter.

Guide on W = nRT x ln(V_f/V_i).

Determine T °K (or Temperature in Kelvin) from PV_f = nRT: 

(101325 N/m²)(0.025 m³) = (1 mol)[8.31451070 (N•m/°K•mol)](T °K) 

gives T °K equal to 304.6631475 °K.

Place values to write 3000 N•m =

(1 mol)[8.31451070 (N•m/°K•mol)](304.6631475 °K)[ln(0.025) − ln(V_i)].

This last simplifies to ln(V_i) as -4.873187374 whose anti-logarithm 

gives Initial Volume or V_i equal to 0.0076489463 m³ or 7.6489463 Liters.