A thermodynamic system is taken from an initial state I with internal energy `U_i=-100J` 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 pat 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),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

A thermodynamic system is taken from an initial state I with internal

1.	A thermodynamic system is taken from an initial state I with internal energy `U_i=-100J` 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 pat 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),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» Correct Answer - B Applying first law of thermodynamics to path iaf `Q_(iaf)=DeltaU_(iaf)+W_(iaf)` `500=DeltaU_(iaf)+200 :. DeltaU_(iaf)=300J` Now, `Q_(ibf)=DeltaU_(ibf)+W_(ib)+W_(bf)` `=300+50+100` `Q_(ib)+Q_(bf)=450J….(1)` Also `Q_(ib)=DeltaU_(ib)+DeltaW_(ib)` `:. Q_(ib)=100+50=150J....(2)` From (1) & (2) `(Q_(bf))/(Q_(ib))=300/150=2`

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