Question

Among the following, the set of parameters that represents path function is:
[A] q + w
[B] q
[C] w
[D] H - TS

Answer 1

HINT: To answer this question, you must approach using the definition of state function and path function. Remember that state function is independent of path whereas path function is dependent upon the path followed. Use this to find out the parameter that represents path function.

COMPLETE STEP BY STEP SOLUTION: We often come across the term state and path function often in thermodynamics. Before answering this question, let us discuss what a state and path function is and how they are different from each other. In simple words, we can say that the property whose value does not depend on the path that is taken to reach a particular value is known as a state function whereas, the value whose value is dependent upon the path followed by it is known as a path function. Now, let us see the properties given to us in the options.
Firstly, we have q + w.
We know that the first law of thermodynamics states that-
$\Delta U=q+w$
We should know that $\Delta U$ is the change in internal energy of the system and it is a function of temperature and volume. ‘q’ is the heat absorbed or released and ‘w’ is the work done. Internal energy is independent of the value of the path followed by it. So, it is a state function. Then, we have q. It is the heat absorbed or released. It is dependent upon the path followed and thus is positive or negative depending upon whether heat is absorbed or released by the system. Therefore, q is a path function. Next we have w that is the work done. Work done is a path dependent function and thus is a path function. And lastly, we have H - TS. We know that in thermodynamics, we can write Gibbs free energy at standard state in terms of standard enthalpy, entropy and temperature as-
$\Delta G=\Delta H-T\Delta S$
Gibbs free energy is a state function as it is independent of the path followed.
We can understand from the above discussion that heat and work done are path functions among the given parameters.

Therefore, the correct answer is option [B] q and [C] w.

NOTE: According to the first law of thermodynamics, if a system is subjected to any cyclic transformation, the sum of heat and work involved is zero.
$\oint{dq+\oint{dw=0}}$
As work done and heat energy both are a path function, their cyclic integration is zero thus, the above statement holds true.