The number of properties which are state function among the following is Pressure, Volume , Temperature,Heat, Work , Entropy, Enthalpy , Free energy, Internal energy,`C_(p)` and`C_(v)`.

Answer

To determine the number of state functions among the given properties, we need to understand the distinction between state functions and path functions.

### Step-by-Step Solution:

1. **Define State Functions**:
State functions are properties that depend only on the state of a system, not on how it reached that state. They are determined by the initial and final conditions of the system.

2. **List the Given Properties**:
The properties provided in the question are:
- Pressure
- Volume
- Temperature
- Heat
- Work
- Entropy
- Enthalpy
- Free Energy
- Internal Energy
- \(C_p\) (heat capacity at constant pressure)
- \(C_v\) (heat capacity at constant volume)

3. **Identify State Functions**:
Now, we will categorize each property as either a state function or a path function:
- **State Functions**:
- Pressure (P)
- Volume (V)
- Temperature (T)
- Entropy (S)
- Enthalpy (H)
- Free Energy (G)
- Internal Energy (U)
- **Path Functions**:
- Heat (q)
- Work (W)
- \(C_p\)
- \(C_v\)

4. **Count the State Functions**:
From the list above, we have identified the following state functions:
- Pressure
- Volume
- Temperature
- Entropy
- Enthalpy
- Free Energy
- Internal Energy

This gives us a total of **7 state functions**.

5. **Conclusion**:
Therefore, the number of properties that are state functions among the given list is **7**.