Question

According to the first Law of Thermodynamics which of the following quantities represents change in a state function?
A. ${q_{rev}}$
B. ${q_{rev}} - {W_{rev}}$
C. $\dfrac{{{q_{rev}}}}{{{W_{rev}}}}$
D. ${q_{rev}} + {W_{rev}}$

Answer 1

State Functions can be described as the quantities or functions which depend on the specific values at the current equilibrium thermodynamic state. To explain it in simpler terms, a state function varies only in accordance with the values taken at specific intervals, rather than depending on the path which was followed to reach the final values.

Complete step by step answer:
Before we move forward with the solution of this question, let us first understand some basic important concepts.
${W_{rev}}$ is basically the reversible work done in a thermodynamic process. To put it in simpler terms, reversible work is basically the amount of work we would need to do to achieve the initial conditions of the thermodynamic reaction. Since reversible work depends only on the initial and final conditions of the thermodynamic process, it is a state function.
${q_{rev}}$ is basically the reversible heat in a thermodynamic process. To put it in simpler terms, it is the heat that is generated by the reversing of the thermodynamic process. It results in the initial state of q once the process is completely reversed. ${q_{rev}}$ is a path dependent function.
Now moving back to the question, one of the examples of state function is the change in internal energy. This quantity is dependent only on the initial and final states of the reaction. Internal energy is represented by $\Delta U$ . According to the First Law of Thermodynamics, the mathematical equation for calculating the change in internal energy is given by:
$\Delta U = q + W$
Since $\Delta U$ is a state function, the change in state function can be represented by ${q_{rev}} + {W_{rev}}$ .

Hence, Option D is the correct option.

Note:
Internal energy, enthalpy, and entropy are examples of state quantities because they quantitatively describe an equilibrium state of a thermodynamic system, regardless of how the system arrived in that state.