Related Problems with Solutions
Problem 4 : Calculate the work done (in joules) when 1 mole of an ideal gas expands isothermally at 298 K from a volume of 5 liters to 10 liters against a constant external pressure of 2 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 (1 mole 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 = 5 liters, Vf = 10 liters).
W = -(1 mole) * 8.314 J/(mol•K) * 298 K * ln(10/5) W = -8.314 J/K * 298 K * ln(2) W ≈ -8.314 J/K * 298 K * 0.693 W ≈ -1,167.93 J ≈ -1.17 kJ
So, the work done during the isothermal expansion is approximately -1.17 kJ.
