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

`(a)` AB is an isothermal process. Hence,
`DeltaU_(AB)=0`
and ` QU_(AB)=W_(AB)=700J`
`(b)` BC is an adiabatic process. Hence.
`QU_(BC)=0`
`W_(Bc)=400J` (given)
` DeltaU_(BC)=W_(Bc)=-400J`
ABC is a cyclic process and internal enery is a state function. Therefore,
`DeltaU_(Wholecycle)=0 DeltaU_(AB)+DeltaU_(BC)+DeltaU_(CA)`
and from first law of thermodynamics,
`Q_(AB)+Q_(BC)+Q_(CA)=W_(AB)+W_(BC)+DeltaW_(CA)`
Substituting the values ,
`700+0-100=700+400+DeltaW_(CA)`
`therefore` `DeltaW_(CA)=-500J`
Negative sign implies that work is done on the gas.