Statement - `1`: An ideal gas has infinitely many molar specific heats.
Statement-`2`: Specific heat is amount of heat needed to raise the temperature of `1` mole of gas by `1K`.

Options

A. Statement -`1` is True , Statement -`2` is True , Statement -`2` is correct explanation for Statement - `1`
B. Statement -`1` is True , Statement -`2` is True , Statement -`2` is not correct explanation for Statement - `1`
C. Statement -`1` is True , Statement -`2` is False.
D. Statement -`1` is False , Statement -`2` is True.

Answer

To solve the question, we need to evaluate the truth of both statements regarding ideal gases and specific heat.

### Step 1: Analyze Statement 1
**Statement 1**: An ideal gas has infinitely many molar specific heats.

- An ideal gas is characterized by two specific heats: the specific heat at constant volume (Cv) and the specific heat at constant pressure (Cp).
- While it is true that these two specific heats can be calculated for various processes, the term "infinitely many molar specific heats" suggests that there are an infinite number of distinct values for specific heat, which is misleading.
- In reality, for a given ideal gas, the specific heats are defined for specific processes (isothermal, isochoric, and isobaric), but they do not imply an infinite number of distinct values.

**Conclusion**: Statement 1 is **false**.

### Step 2: Analyze Statement 2
**Statement 2**: Specific heat is the amount of heat needed to raise the temperature of 1 mole of gas by 1K.

- The definition provided in Statement 2 aligns with the standard definition of molar specific heat.
- Molar specific heat is indeed defined as the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius (or equivalently, one Kelvin, since the size of the degree is the same in both scales).
- This definition is universally accepted in thermodynamics.

**Conclusion**: Statement 2 is **true**.

### Final Conclusion
- Statement 1 is false.
- Statement 2 is true.

Thus, the answer to the question is that Statement 1 is false and Statement 2 is true.

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