Which of the following is a path function? a.) Work b.) Specific volume c.) Pressure d.) Temperature
Hint: In thermodynamics, a quantity that is well defined so as to describe the path of a process through the equilibrium state space of a thermodynamic system is termed a process function, or, alternatively, a process quantity, or a path function. Path functions are properties or quantities whose values depend on the transition of a system from the initial state to the final state.
Complete answer: Work performed by a system can be defined as the energy transferred by the system to its surroundings, by a mechanism through which the system can spontaneously exert macroscopic forces on its surroundings. Work done in a system depends on what path is chosen for performing task to go from state 1 to state 2. So, work is a path function as different routes give different quantities. The specific volume of a substance can be defined as the ratio of the substance's volume to its mass. It does not depend on that path taken as it is measured for a state and not a route. So, it is a state function. Pressure can be defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed. It does not depend on that path taken as it is measured for a state and not a path. So, it is a state function. Temperature is a state function as it is one of the values used to define the state of an object. Temperature is dependent only on the final and initial values, not on the path taken to establish the values. Hence, it is also a state function. Hence, the correct answer is that work is a path function. So, the correct answer is “Option A”.
Note: A state function or function of state can be given as a function defined for a system relating several state variables or state quantities that depends only on the current equilibrium state of the system, for example a gas. Temperature, pressure, internal energy, etc. all are state functions.
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