Which of the following statements is // are correct ?

Options

A. `A` gas has two specific heats only
B. A materials will have only one specific heat, if and only if its coefficient of thermal expansion is equal to zero.
C. A gas has infinite number of specific heats.
D. None of these

Answer

To determine which of the statements regarding specific heats of gases is correct, we will analyze each statement one by one.

### Step 1: Analyze the First Statement
The first statement claims that a gas has two specific heats only.

- **Explanation**: In thermodynamics, gases are characterized by two specific heats:
- \( C_v \) (specific heat at constant volume)
- \( C_p \) (specific heat at constant pressure)

Since these are the only two specific heats defined for gases, this statement is **correct**.

### Step 2: Analyze the Second Statement
The second statement suggests that a material will have only one specific heat if and only if its coefficient of thermal expansion is equal to 0.

- **Explanation**: The specific heat of a material is a measure of the amount of heat required to change its temperature. The coefficient of thermal expansion measures how much a material expands when heated. There is no direct relationship between the coefficient of thermal expansion and specific heat. Therefore, this statement is **incorrect**.

### Step 3: Analyze the Third Statement
The third statement claims that a gas has an infinite number of specific heats.

- **Explanation**: While it is true that specific heats can vary with temperature and pressure, gases are conventionally defined by the two specific heats \( C_v \) and \( C_p \). Thus, stating that a gas has an infinite number of specific heats is misleading and **incorrect**.

### Conclusion
Based on the analysis:
- The first statement is **correct**.
- The second statement is **incorrect**.
- The third statement is **incorrect**.

Thus, the correct option is **A**.

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