Among the following the number of state variable is
Internal energy (U), Volume (V), Heat (q), Enthalpy (H)

We need to identify how many of the given quantities — Internal energy (U), Volume (V), Heat (q), and Enthalpy (H) — are state variables (also called state functions).

A state variable (or state function) is a thermodynamic property whose value depends only on the current state of the system and not on the path taken to reach that state. In contrast, a path function depends on the specific process or path followed.

Internal energy (U): Internal energy depends only on the state of the system (temperature, pressure, composition). It does not depend on how the system reached that state. So U is a state variable.

Volume (V): Volume is a property that is uniquely determined by the state of the system. Regardless of how the system was brought to a particular state, the volume at that state is fixed. So V is a state variable.

Heat (q): Heat is energy transferred between a system and its surroundings due to a temperature difference, and its value depends on the path taken. For example, in an isothermal expansion vs. an adiabatic expansion followed by heating, the amount of heat exchanged is different even if the initial and final states are the same. So q is a path function, not a state variable.

Enthalpy (H): Enthalpy is defined as $$H = U + PV$$, where U, P, and V are all state functions. Since enthalpy is derived from state functions, it is also a state variable.

So among the four quantities, U, V, and H are state variables, while q is not. The number of state variables is 3.

Hence, the correct answer is 3.