**Correct Option: C. The pressure increases** ### Detailed Explanation: **Understanding Boyle's Law:** Boyle's Law states that for a given mass of an ideal gas at constant temperature, the pressure (P) of the gas is inversely proportional to its volume (V). This relationship can be mathematically expressed as: \[ P \propto \frac{1}{V} \] or, more commonly, \[ PV = k \] where \( k \) is a constant for a given amount of gas at a constant temperature. **Step-by-Step Analysis:** 1. **Constant Temperature:** The problem states that the temperature remains constant. This is crucial because Boyle's Law applies specifically under isothermal conditions (constant temperature). 2. **Decreasing Volume:** When the volume of the gas decreases, we can denote the initial volume as \( V_1 \) and the final volume as \( V_2 \) where \( V_2 < V_1 \). 3. **Applying Boyle's Law:** - Initially, we have: \[ P_1 V_1 = k \] - After the volume decreases, we have: \[ P_2 V_2 = k \] - Since \( k \) is constant, we can set the two equations equal to each other: \[ P_1 V_1 = P_2 V_2 \] 4. **Rearranging the Equation:** - From the equation \( P_1 V_1 = P_2 V_2 \), we can express \( P_2 \) in terms of \( P_1 \): \[ P_2 = \frac{P_1 V_1}{V_2} \] - Since \( V_2 < V_1 \), the fraction \( \frac{V_1}{V_2} \) is greater than 1. Therefore, \( P_2 \) must be greater than \( P_1 \): \[ P_2 > P_1 \] 5. **Conclusion:** Thus, when the volume of the gas decreases while the temperature remains constant, the pressure of the gas increases. ### Why Other Options Are Incorrect: - **Option A: The pressure decreases** - This option contradicts Boyle's Law. If the volume decreases, the pressure must increase, not decrease. - **Option B: The pressure remains constant** - This option is also incorrect because it ignores the inverse relationship between pressure and volume. If the volume changes, the pressure cannot remain constant unless the temperature changes, which is not the case here. - **Option D: The pressure becomes zero** - This option is not physically possible under normal conditions. A gas cannot have zero pressure unless it is in a vacuum. Decreasing the volume of a gas at constant temperature will not lead to zero pressure; instead, it will lead to an increase in pressure. ### Summary of Key Points: - Boyle's Law states that pressure and volume are inversely related at constant temperature. - Decreasing the volume of a gas increases its pressure. - The relationship can be expressed mathematically as \( PV = k \). - Understanding the implications of constant temperature is crucial for applying Boyle's Law correctly. This thorough understanding of Boyle's Law will help you tackle related problems effectively in your exams!