Question

Calculate the irreversible work done by a gas expanding adiabatically from an initial volume of 1 L to a final volume of 5 L against a constant external pressure of 2 atm, assuming that the gas is initially at a temperature of 300 K and that its final temperature is 400 K.

Answer 1

To calculate the irreversible work done by a gas expanding adiabatically against a constant external pressure, we can use the formula:W = -P_ext * Vwhere W is the work done, P_ext is the constant external pressure, and V is the change in volume.Given the initial volume  V1  is 1 L and the final volume  V2  is 5 L, we can calculate the change in volume:V = V2 - V1 = 5 L - 1 L = 4 LThe external pressure  P_ext  is given as 2 atm. To convert the volume from liters to cubic meters, we can use the conversion factor 1 L = 0.001 m:V = 4 L * 0.001 m/L = 0.004 mNow, we need to convert the pressure from atm to Pascal  Pa  using the conversion factor 1 atm = 101325 Pa:P_ext = 2 atm * 101325 Pa/atm = 202650 PaNow we can calculate the work done:W = -P_ext * V = -202650 Pa * 0.004 m = -810.6 JTherefore, the irreversible work done by the gas expanding adiabatically is -810.6 Joules. The negative sign indicates that the work is done by the gas on the surroundings.