How many of the following are state function:
(i) Internal energy (ii) Heat (iii) Enthalpy (iv) Entropy
(v) Pressure (vi) Temp. (vii) volume (viii) work
(ix) specific heat capacity (x) molar heat capacity

Answer

To determine how many of the given terms are state functions, we need to classify each term based on whether it depends on the state of a system or the path taken to reach that state.

### Step-by-Step Solution:

1. **Understanding State Functions**:
- State functions are properties that depend only on the state of a system, not on how that state was reached. Examples include internal energy, enthalpy, entropy, pressure, temperature, and volume.

2. **Classifying Each Term**:
- **(i) Internal Energy**: This is a state function because it depends only on the initial and final states of the system.
- **(ii) Heat**: This is not a state function; it is a path function because it depends on the process taken to transfer energy.
- **(iii) Enthalpy**: This is a state function as it depends only on the state of the system.
- **(iv) Entropy**: This is also a state function, as it depends on the state of the system.
- **(v) Pressure**: This is a state function; it is a property of the system at equilibrium.
- **(vi) Temperature**: This is a state function; it defines the thermal state of the system.
- **(vii) Volume**: This is a state function; it is a measure of the space occupied by the system.
- **(viii) Work**: This is not a state function; it is a path function because it depends on the process taken to do work.
- **(ix) Specific Heat Capacity**: This is a state function; it is defined for a given substance at a specific state.
- **(x) Molar Heat Capacity**: This is also a state function; it depends on the state of the substance.

3. **Counting the State Functions**:
- From the classification, the state functions are:
- Internal Energy (i)
- Enthalpy (iii)
- Entropy (iv)
- Pressure (v)
- Temperature (vi)
- Volume (vii)
- Specific Heat Capacity (ix)
- Molar Heat Capacity (x)

- Total number of state functions = 8

### Final Answer:
There are **8 state functions** among the given terms.