50 cal of heat should be supplied to take a system from the state A to the state B through the path ACB as shown in Figure. The quantity of heat to be supplied to take it from A to B via ADB.

Explanation

process ACB:
`Delta_(ACB)=DeltaW_(AC)+DeltaW_(CB)`
`=50xx10^3xx(400-200)xx10^-6+0`
`=10J=(10)/(4.2)=2.4cal`
`DeltaQ=50cal`
`DeltaQ=DeltaU+DeltaW=U_B-U_A+DeltaW`
`50=(U_B-U_A)+2.4`
`U_B-U_A=47.6cal`
Process ADB:
`DeltaW_(ADB)=DeltaW_(AD)+DeltaW_(DB)`
`=0+155xx10^3xx(400-200)xx10^-6`
`=31J=(31)/(4.2)=7.4cal`
`DeltaQ=DeltaU+DeltaW=U_B-U_A+7.4`
`=47.6+7.4`
`=55cal`