Exemplar Problems
Problem 5 : Calculate the work done (in joules) when 2 moles of an ideal gas expand isothermally at 298 K from a volume of 10 liters to 20 liters against a constant external pressure of 5 atm.
Solution :
The work done (W) during an isothermal expansion of an ideal gas can be calculated using the formula: W = -nRT ln(Vf/Vi)
Where:
- n is the number of moles of the gas (2 moles in this case).
- R is the ideal gas constant (8.314 J/(mol•K)).
- T is the temperature in Kelvin (298 K).
- Vi and Vf are the initial and final volumes, respectively (Vi = 10 liters, Vf = 20 liters).
W = -2 moles * 8.314 J/(mol•K) * 298 K * ln(20/10) W = -2 * 8.314 J/K * 298 K * ln(2) W ≈ -2 * 8.314 J/K * 298 K * 0.693 W ≈ -3,940.88 J ≈ -3.94 kJ
So, the work done during the isothermal expansion is approximately -3.94 kJ.
BETA
