Question

One mole of a prefect put throught a cycle consiting
of the following three reversible steps :
(CA) Isothermal comoression from 2 atm and 10 litres to 20 atm and litre.
(AB ) Isobaric expansion to return the gas to the origanl volume of 10
litre with T going from `T_(1)` to `T_(2)`
(BC) Cooling at constant volume to bring the gas to the origanl pressure lt brgt and temperature .
The steps are shown schematically in the figure shown.
Calculate `T_(1)` to `T_(2)`.
(b) Calculate `DeltaU, q and will be in calories , for each step and for the cycle .

Answer 1

Correct Answer - (a)`T_(1) = 243.60; T_(2)= 2436.0 K`, (b) `DeltaU = 0; q= - w = + 3262.88 cal`
(a)`" "(PV)/(R)= (20 xx1)/(0.0821) = 243.6 K`
`T_(2) = (20 xx 10 )/(0.021) = 2436.0 K`
(b) CA(Isothermal )
`W_(1) = - 2.303 xx 2 xx 243.6 log .(2)/(20)= 1122`
BC(Isochoric )
`W_(2) = 0`
AB(Isochoric)
`W_(3) = - RDeltaT = - 4384.9 cal`
For complete cycle
`W = W_(1) + W_(2) + W_(3) = 3262. 888 cal`