The work done by an ideal gas in an isothermal expansion from volume V₁ to volume V₂ is given by the formula: W = nRT lnV₂/V₁). Standard atmospheric pressure 1 atm) is 101.3 kPa. If 1.0 L of He gas at room temperature 20^oC) and 1.0 atm of pressure is compressed isothermally to a volume of 100 mL, how much work is done on the gas? A) 5.6 kJ B) 4.7 × 10² J C) 4.7 × 10² kJ D) 2.3 × 10² kJ E) 2.3 × 10² J

Question

Quizplus · Accepted Answer

The work done on the gas is calculated using the formula W = nRT ln(V2/V1). First, convert the volumes to the same units (1.0 L = 1000 mL, so V1 = 1000 mL and V2 = 100 mL). The number of moles n can be found using the ideal gas law PV = nRT, where P = 1 atm = 101.3 kPa, V = 1.0 L, R = 8.314 J/mol·K, and T = 293 K (20°C). Solving for n gives n = PV/RT. Then, substitute n, R, T, V1, and V2 into the work formula to find W. The correct answer is approximately 2.3 × 10^2 J.

The Work Done by an Ideal Gas in an Isothermal