An ideal gas expands isothermally along AB and does `700J` of work. How much heat does the gas exchange along AB? The gas then expands adiabarically along BC and does `400J` of work. When the gas returns to A along CA, it exhausts `100J` of heat to the surroundings. How much work is done on the gas along this path?

Explanation

As AB is an isothermal process, therefore, `dU_(AB)=0`
According to first law of thermodynamics.
`dQ_(AB)=dU_(AB)+dW_(AB)`
`dQ_(AB)=0+700= 700J`
As the gas returns finally to state A, the process must be cyclic
`:. dU_(AB)+dU_(BC)+dU_(CA)=0`
As the gas returns finally to state A, the process must be cyclic
`:. dU_(AB)+dU_(BC)+dU_(CA)=0`
As BC is adiabatic process,
`:. dQ_(BC)=0`
`:. dQ_(AB)+dQ_(BC)+dQ_(CA)=(dU_(AB)+dU_(BC)+dU_(CA))`
`+(dW_(AB)+dW_(BC)+dU_(CA))`
`700+0-100=0+(700+400+dW_(CA)`
`:. dW_(CA)= -500J`