Question

When the state of a system changes from A to B adiabatically the work done on the system is 322 Joule. If the state of the same system is changed from A to B by another process, and heat required is 50 calories of heat, then find work done on the system in this process? (J=4.2 J / c a l)
(A) 98J
(B) 38.2 J
(C) 15.9 J
(D) 16.9 J

Answer 1

Hint :The first law of thermodynamics is a thermodynamic adaptation of the concept of conservation of energy, differentiating between two types of energy transmission, heat and thermodynamic work, and linking them to a function of a body's state called Internal energy. We use the First law of thermodynamics to solve this problem.

Complete Step By Step Answer:
The law of conservation of energy holds that an isolated system's total energy remains constant; energy can be transferred from one form to another, but it cannot be generated or destroyed.
The first law is frequently used to describe a thermodynamic process that does not involve the transfer of stuff.
 $ \Delta U = Q \pm W $
where $ \Delta U $ signifies the change in a closed system's internal energy, Q signifies the amount of energy given to the system as heat, and W signifies the amount of thermodynamic work done on the system's surroundings. Perpetual motion machines of the first sort are impossible, to put it another way.
Using Given relation,
 $ {{\text{W}}_{{\text{AB}}({\text{ adiabatic }})}} = - 322\;{\text{J }} $ (The work done on the system)
 $ {{\text{Q}}_{{\text{AB}}({\text{ other }})}} = + {\mathbf{100}}{\text{cal}} = 100 \times 4.2\;{\text{JCa}}{{\text{l}}^{ - 1}} = + 420\;{\text{J}} $
Now let us suppose the change in internal energy be $ \Delta {U_{AB}} $
Hence,
 $ {\mathbf{Q}} = \Delta {\text{U}} + {\text{W}} $
\[{{\text{Q}}_{{\text{AB}}({\text{adia}})}} = \Delta {{\text{U}}_{{\text{AB}}}} + ( - 322) = 0\]
Hence,
 $ {{\text{Q}}_{{\text{AB}}({\text{ other }})}} = \Delta {{\text{U}}_{{\text{AB}}}} + {{\text{W}}_{{\text{AB}}({\text{other}})}} = 420 $
Now when we subtract the above 2 equation we get,
 $ {{\text{W}}_{{\text{AB}}({\text{ other }})}} + 322 = 420 $
 $ \; \Rightarrow {{\text{W}}_{{\text{AB}}({\text{ other }})}} = 98{\text{ Joules}}{\text{. }} $
Hence option A is correct.

Note :
The work done on the system is $ {{\text{W}}_{{\text{AB}}({\text{ adiabatic }})}} = - 322\;{\text{J }} $ and not 322 J. This is due to the fact that work done on the system is Negative always. An adiabatic process is a sort of thermodynamic process that happens without the passage of heat or mass between the system and its surroundings in thermodynamics. An adiabatic process, unlike an isothermal process, only sends energy to the environment as work.