Question

Two moles of a perfect gas undergo the following processes
(i) a reversible isobaric expansion from (1.0 am, 20.0L) to (1.0 atm, 40.0 L)
(ii) a reversible isochoric change of state from (1.0 atm, 40.0 L) to (0.5 atm, 40.0 L);
(iii) a reversible isothermal compression from (0.5 am, 40.0 L) to (1.0 atm, 20.0 L)
What is the total heat exchange here in Joules?

$ln2=0.7,ln3=1.1,R=1/12Latm/mol,25/3J/molK,1Latm=101J$

Answer 1

Cyclic process:
For cyclic process change in state function must be zero thus
$\Delta E=0$ for this cyclic process
$\Delta E=Q+W$
$Q=-W=w_i+w_{ii}+w_{iii}\left(1\right)$
work done in isobaric process
$w_i=-P\Delta V=-1\times (40-20)=-20Latm$
work done in isochoric process and we know that for isochoric process $dv=0$
$w_{ii}=-pdv=0$
work done in isothermal process:
$pv=nRT=0.5\times 40or1\times 20=20Latm$
$w=-nRTln\frac{v_{intial}}{v_{final}}$

$w_{iii}=-20\times ln\frac{40}{20}$$Latm$
on substituting in (1) we get
$Q=606J$