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Question:

A thermodynamic system is taken from an initial state i with internal energy Ui=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 paths af, ib and bf are Waf=200J, Wib=50J and Wbf=100J respectively. The heat supplied to the system along the path iaf, ib and bf are Qiaf, Qib and Qbf respectively. If the internal energy of the system in the state b is Ub=200J and Qiaf=500J, the ratio Qbf/Qib is ?

Solution:

Ub=200J,Ui=100J
Process iaf
Process W(in Joule) ΔU (in Joule) Q(in Joule)
ia 0
af 200
Net 300 200 500
→Uf=400Joule
Process ibf
Process W(in Joule) ΔU (in Joule) Q(in Joule)
ib 100 50 150
bf 200 100 300
Net 300 150 450
→Qbf/Qib=300/150=2