Question

The internal energy U is a unique function of any state because change in U.
A) Does not depends upon path
B) Depends upon path
C) Corresponds to adiabatic process
D) Corresponds to an isothermal process

Answer 1

Unique function is the one which does not depend on the path followed. Check if Internal Energy of a body or system depends on the path followed for any process or Not. Do remember that Internal Energy in the system is not all the energy. Internal energy is the property or state function that defines the energy of a substance in the absence of effects due to capillarity and external electric, magnetic, and other fields.

Complete step by step solution: Internal energy and enthalpy depends on temperature. They do not depend on pressure and volume. Unlike the work done by the system, the Internal energy is independent of the path followed. Hence it is known as a unique function.

Therefore option A is the correct option.

An adiabatic process is one in which there is no exchange of heat by the system to the surrounding. The first law of thermodynamic states that for an adiabatic process all the change in the internal energy is in the form of the work done.
For an isothermal process the temperature is constant. As internal energy is a state function which depends on temperature hence for an isothermal process the internal energy will be zero.

Note: It must be remembered that internal energy of the system depends on the initial and final state of the system. When the temperature of the system rises, the internal energy also rises. Internal energy is identified by the degree of randomness of the molecules. The total internal energy in the system includes the kinetic energy as well as potential energy.