Question

Which of the following is not a thermodynamical function. (A) Enthalpy (B) Work done (C) Gibb's energy (D) Internal energy

Short answer

The non-thermodynamical function among the given options is (B) Work done, as it depends on the path taken and not solely on the state of the system.

Step-by-step solution

Define Enthalpy

Enthalpy (H) is a state function that describes the total energy of a system, including both its internal energy and the energy associated with its pressure and volume. Mathematically, it is defined as: \[H = U + PV\] where U is the internal energy, P is the pressure, and V is the volume of the system. Since enthalpy is a combination of state functions, it is also a state function.

Define Work Done

Work done (W) is not a state function. It refers to the energy transferred to or from a system due to an external force or pressure acting upon it. The work done depends on the path taken during the process and not just the initial and final states of the system. Mathematically, it can be expressed for a reversible process in a closed system as: \[W = -\int_{V_1}^{V_2} PdV\] where V1 and V2 are the initial and final volumes, and P is the pressure. Since work done depends on the path taken, it is not a state function.

Define Gibb's Energy

Gibb's energy (G) is a state function that represents the maximum work that a system can perform in a reversible process at constant temperature and pressure. Mathematically, it is defined as: \[G = H - TS\] where H is enthalpy, T is the temperature, and S is the entropy of the system. Since Gibb's energy is a combination of state functions, it is also a state function.

Define Internal Energy

Internal energy (U) is a state function that represents the total energy of a system, including the kinetic energy due to the motion of its particles and potential energy due to their interaction. It depends only on the state of the system and not the path taken.

Identify the Non-Thermodynamical Function

Based on the definitions provided in Steps 1-4, we can conclude that the option (B) Work done is not a thermodynamical function, as it depends on the path taken and not solely on the state of the system.