Question

The work done to contract gas in a cylinder is 462 joules.128 joule energy is evolved in the process. What will be the internal energy change in the process
A. +590 joules
B. −334 joules
C. +334 joules
D. -590 joules

Answer 1

Hint: The first law of thermodynamics states that energy can neither be generated nor eliminated but can be converted from one form to another.
Thus, the disappearance of one form of energy leads to the appearance of an equivalent amount of energy in some other form.

Formula Used:
\[{\rm{\Delta U=q+w}}\] where
\[{\rm{\Delta U}}\]=change in internal energy
q=heat evolved and
w=work done

Complete step-by-step answer:
In this reaction, it is given that during a process of compression, 128 joules of heat evolved.
During compression, work is performed on the system. So, heat is lost by the system.
So, the magnitude of heat evolved during this process will be negative.
As the work is performed on the system by the surroundings, w will be positive.
So, the internal energy change is given by the expression: -
\[{\rm{\Delta U = q + w}}\] where
\[{\rm{\Delta U}}\]=change in internal energy
q=heat evolved=(-128) joules
w=work performed =462 joules
\[{\rm{\Delta U = }}\left( {{\rm{ - 128 + 462}}} \right)\] joules
=334 joules

So, option C is correct.

Note: While attempting the question, one must remember that the process of contraction of gas in a cylinder involves the compression of gas.
During compression, work is performed on the system by the surroundings. So, the work performed, w is positive. In this process, heat is evolved i.e., heat is lost by the system. So, q is negative.