At constant temperature, in a given mass of an ideal gas

Options

A. the ratio of pressure and volume always remains constant
B. volume always remains constant
C. pressure always remains constant
D. the product of pressure and volume always remains constant.

Explanation

To solve the question regarding the behavior of an ideal gas at constant temperature, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Context**: We are dealing with an ideal gas at constant temperature. This implies that we are looking at a scenario where the temperature does not change while examining the gas's properties.

2. **Recall Boyle's Law**: Boyle's Law states that for a given mass of an ideal gas at constant temperature, the pressure (P) and volume (V) of the gas are inversely related. This means that if the volume increases, the pressure decreases, and vice versa.

3. **Formulate the Relationship**: According to Boyle's Law, the product of pressure and volume (PV) remains constant. Mathematically, this can be expressed as:
\[ PV = k \]
where \( k \) is a constant for a given mass of gas at a constant temperature.

4. **Analyze the Options**: Now, we can evaluate the provided options:
- **Option A**: The ratio of pressure and volume always remains constant. (Incorrect)
- **Option B**: Volume always remains constant. (Incorrect)
- **Option C**: Pressure always remains constant. (Incorrect)
- **Option D**: The product of pressure and volume always remains constant. (Correct)

5. **Conclusion**: Based on Boyle's Law, the correct answer is that the product of pressure and volume of a given mass of an ideal gas at constant temperature is always constant. Therefore, the correct option is **D**.

### Final Answer:
The product of pressure and volume always remains constant (Option D).

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