Question

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

Answer 1

$U_b=200J,U_i=100J$
Process iaf

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

$\Rightarrow U_f=400Joule$
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

$\Rightarrow \frac{Q_{bf}}{Q_{ib}}=\frac{300}{150}=2$