Question

4.0 mol of ideal gas at 2 and 25 C expands isothermally to 2 times o of its original
volume against the external pressure of 1 atm. Calculate work done. If the same gas
expands isothermally in a reversible manner, then what will be the value of work done.
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Answer 1

Given info : 4.0 mol of ideal gas at 2 and 25 C expands isothermally to 2 times o of its original

volume against the external pressure of 1 atm.

To find : The work done by the gas.

if the same gas expands isothermally in a reversible manner, the value of work done by the gas.

solution : no of moles, n = 4

initial pressure, Pi = 2 atm

final pressure, Pf = 1 atm

Temperature,T = 25°C = 298K

initial volume, Vi = nRT/Pi

= 4 × 0.082 × 298/2

= 2 × 0.082 × 298

= 48.872 L

final volume, Vf = PiVi/Pf

= (2 atm × 48.872 L)/(1 atm)

= 97.744 L

now work done = -Pext(Vf - Vi)

= -1 × (97.744 - 48.872)

= -48.872 atm.L

= - 4951.995 J

= 4.951995 kJ

[ we know, 1 atm.L = 101.325 J ]

for isothermal expansion,

work done , W = -2.303nRT log[Vf/Vi]

= -2.303 × 4 × 25/3 × 298 log [97.744/48.872]

[ where R = 25/3 J/K/mol]

= -6886.50266 J

= -6.8865 kJ