Question

Which of the following is a state function?
A. $\text{q }\\!\\!\times\\!\\!\text{ w}$
B. $\text{q + w}$
C. $\dfrac{{{\text{q}}^{\text{2}}}}{{{\text{w}}^{\text{2}}}}$
D. $\sqrt{\text{qw}}$

Answer 1

Hint: To answer this question we need to know what are quantities that are represented by the variables. Once we know, we can find out the property denoted by them. Then the property can be categorized as a state function or not.

Complete step by step answer:
In thermodynamics, a state function or function of state or point function is a function defined for a system relating several state variables or state quantities that depends only on the current equilibrium state of the system.
In thermodynamics, q denotes the net heat transfer and w denotes the net work done. By q we mean the sum of all heat transferred into and out of the system. And by w we mean the sum of all work done on or by the system. The sum of q and w is internal energy. Though q and w are path functions and are not state functions. Both the quantities depend upon the path followed by the reaction or process.
But the sum of q and w which is $\text{q + w}$ denotes the internal energy, is a state function. Internal energy is a state function as it does not depend upon the path but the initial and final points.
Hence, the correct answer to the question is Option B.

Note: Internal energy that is mentioned in the answer is the energy contained within the system. It is the energy which is necessary to create or prepare the system in any given state, but does not include the kinetic energy of motion of the system as a whole, nor the potential energy of the system as a whole. This is because of the external force fields which includes the energy of displacement of the system’s surroundings.