A gas has more than one specific heats, whereas a liquid and solid have only one. Why?
OR
Why gas has two principle specific heat capacties.

Answer

To understand why a gas has more than one specific heat capacity while solids and liquids have only one, we need to delve into the behavior of different states of matter under heating.

### Step-by-Step Solution:

1. **Understanding Specific Heat Capacity**:
- Specific heat capacity is defined as the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius (or one Kelvin).
- It can vary depending on the conditions under which the heat is added.

2. **States of Matter**:
- Matter exists in three primary states: solid, liquid, and gas.
- Solids and liquids are generally incompressible, meaning their volume and density do not change significantly with pressure.

3. **Behavior of Solids and Liquids**:
- When heat is added to a solid or liquid, the temperature increases without a change in volume or pressure.
- Therefore, there is only one specific heat capacity for solids and liquids, as the heat added only contributes to temperature change.

4. **Behavior of Gases**:
- Gases, on the other hand, are compressible. When heat is added to a gas, both its temperature and volume can change.
- This leads to two distinct processes for heating a gas: heating at constant volume and heating at constant pressure.

5. **Constant Volume Heating**:
- When a gas is heated at constant volume, the heat added increases the internal energy of the gas, leading to an increase in temperature. This is represented by the specific heat capacity at constant volume (C_v).

6. **Constant Pressure Heating**:
- When a gas is heated at constant pressure, the gas expands, doing work on its surroundings. The heat added not only increases the internal energy but also does work, which is represented by the specific heat capacity at constant pressure (C_p).
- The relationship between C_p and C_v is given by the equation C_p = C_v + R, where R is the gas constant.

7. **Conclusion**:
- Thus, gases have two specific heat capacities (C_p and C_v) because they can change both temperature and volume with the addition of heat, whereas solids and liquids only change temperature without a change in volume or pressure.