Question

A cylinder with a volume of 2.5 L contains 1.5 moles of an ideal gas at a pressure of 5 atm. The gas is allowed to expand isothermally against a constant external pressure of 1 atm until the volume doubles. Calculate the work done by the gas during the expansion process.

Answer 1

To calculate the work done by the gas during the isothermal expansion, we can use the formula:W = -P_ext * Vwhere W is the work done, P_ext is the external pressure, and V is the change in volume.Since the volume doubles, the final volume  V_f  will be:V_f = 2 * V_i = 2 * 2.5 L = 5 LThe change in volume  V  is:V = V_f - V_i = 5 L - 2.5 L = 2.5 LNow we can calculate the work done:W = -P_ext * V = -1 atm * 2.5 LTo convert the work done to joules, we need to use the conversion factor: 1 Latm = 101.325 JW = -1 atm * 2.5 L *  101.325 J / 1 Latm  = -253.3125 JSo, the work done by the gas during the expansion process is approximately -253.31 J. The negative sign indicates that the work is done by the gas  expansion .