Question

A thermodynamic system is taken from an initial state $i$ with internal energy $U _{ i }=100 \,J$ to the final state $f$ along two different paths iaf and $ibf$, as schematically shown in the figure. The work done by the system along the paths $a f,ib$ and $bf$ are $W _{ af }=200 \,J , W _{ ib }=50 \,J$ and $W _{ bf }=100\, J$ respectively. The heat supplied to the system along the path iaf, $ib$ and $bf$ are $Q _{ \text{iaf}}$, $Q _{\text{ib }}$ and $Q _{\text {bf }}$ respectively. If the internal energy of the system in the state $b$ is $U _{ b }=200 \,J$ and $Q _{\text {iaf }}=500 \,J$, the ratio $Q _{\text{bf}} / Q _{\text{ib}}$ is

Answer 1

$U _{ b }=200\, J ,$
$ U _{ i }=100\, J$
Process iaf

Process	W(in Joule)	$\Delta U$ ( in Joule )s	Q(in Joule)
ia		0
af		200
Net	300	200	500

$\Rightarrow U _{ f }=400$
Joule Process ibf

Process	W(in Joule)	$\Delta U$ ( in Joule )	Q(in Joule)
ib	100	50	150
bf	200	100	300
Net	300	150	450