Question

Ten liters of a monoatomic ideal gas at 25^o C and 10 atm pressure are expanded to a final pressure of 1 atm. The molar heat capacity of the gas at constant volume, Cv, is 3/2R and is independent of temperature. Calculate the work done, the heat absorbed, and the change in U and H for the gas if the process is carried out

(1) isothermally and reversibly, and

(2) adiabatically and reversibly.

Having determined the final state of the gas after the reversible adiabatic expansion, verify that the change in U for the process is independent of the path taken between the initial and final states by considering the process to be carried out as:

i. An isothermal process followed by a constant-volume process

ii. A constant-volume process followed by an isothermal process

iii. An isothermal process followed by a constant-pressure process

iv. A constant-volume process followed by a constant-pressure process

v. A constant-pressure process followed by a constant-volume process

Answer 1

1) for isothermal and reversible process:

work done = = 1*8.14*298*ln(10) = 5.6kJ

U is proportional to change in temperature, so delta(U)= 0 as T is constant.

U=Q-W, so Q= 5.6kJ

delta(H) is also zero as delta (T) is zero

2) Adiabatic reversible process:

for an adiabatic process, no heat is added or removed from the system, so Q=0

we have where =5/3 for a monoatomic gas. putting the values we get, V₂=40 litres

work done = where K =PV^gamma = constant

putting values W = -90 J

Also W=delta(U) for adiabatic process

in the figure the five cases for the adiabatic process have addressed where the initial anf final points are fixed. the adiabatic process has been shown in dotted lines and the solid lines depict the processes named (i)-(v)