If the pressure of an ideal gas at constant volume is decreased by 20% then the percentage change in temperature will be 

Options

A. 20% increase
B. 20% decrease
C. 80% increase
D. 80% decrease

Answer

To solve the problem, we will use the relationship between pressure and temperature for an ideal gas at constant volume, which is described by Gay-Lussac's Law. According to this law, the pressure of a gas is directly proportional to its absolute temperature when the volume is held constant.

### Step-by-Step Solution:

1. **Understand the Initial Conditions**:
- Let the initial pressure \( P_1 = 100 \) (arbitrary units).
- Since the pressure is decreased by 20%, the new pressure \( P_2 \) will be:
\[ P_2 = P_1 - 0.20 \times P_1 = 100 - 20 = 80 \]

2. **Use Gay-Lussac's Law**:
- According to Gay-Lussac's Law:
\[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \]
- Rearranging this gives:
\[ T_2 = \frac{P_2 \times T_1}{P_1} \]

3. **Substitute the Values**:
- Substitute \( P_1 \) and \( P_2 \) into the equation:
\[ T_2 = \frac{80 \times T_1}{100} = 0.8 T_1 \]

4. **Calculate the Change in Temperature**:
- The change in temperature \( \Delta T \) is given by:
\[ \Delta T = T_2 - T_1 = 0.8 T_1 - T_1 = -0.2 T_1 \]

5. **Calculate the Percentage Change in Temperature**:
- The percentage change in temperature is calculated as:
\[ \text{Percentage Change} = \left( \frac{\Delta T}{T_1} \right) \times 100 = \left( \frac{-0.2 T_1}{T_1} \right) \times 100 = -20\% \]
- Since we are interested in the magnitude of the change, we take the absolute value:
\[ \text{Percentage Change} = 20\% \]

### Final Answer:
The percentage change in temperature is **20%**.

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