At constant temperature the pressure of a gas is inversely proportional to its volume. 1140 litres of a certain gas exerts a pressure of 750 units. If the pressure is increased by 10 units keeping the temperature constant, by how many litres will its volume decrease?


Let's solve this problem step-by-step using the inverse proportionality relationship between the pressure and volume of a gas at constant temperature.

### Given:
- Pressure (\( P_1 \)) = 750 units
- Volume (\( V_1 \)) = 1140 litres
- New pressure (\( P_2 \)) = \( 750 + 10 = 760 \) units
- Temperature is constant.

### To Find:
- The decrease in volume (\( \Delta V \)).

### Step-by-Step Solution:

1. **Inverse Proportionality Relationship:**

   Since the pressure of a gas is inversely proportional to its volume at constant temperature, we can write:

   \[
   P \times V = \text{constant}
   \]

   Therefore, 

   \[
   P_1 \times V_1 = P_2 \times V_2
   \]

   Where:
   - \( P_1 = 750 \) units, \( V_1 = 1140 \) litres
   - \( P_2 = 760 \) units, \( V_2 \) is the new volume.

2. **Calculate the Constant:**

   Using the initial values:

   \[
   750 \times 1140 = 855000
   \]

   So, the constant \( C = 855000 \).

3. **Find the New Volume (\( V_2 \)):**

   Using the relationship:

   \[
   P_2 \times V_2 = C \implies 760 \times V_2 = 855000
   \]

   Solving for \( V_2 \):

   \[
   V_2 = \frac{855000}{760} \approx 1125 \text{ litres}
   \]

4. **Calculate the Decrease in Volume (\( \Delta V \)):**

   The decrease in volume is:

   \[
   \Delta V = V_1 - V_2 = 1140 - 1125 = 15 \text{ litres}
   \]

### Answer:
The volume will decrease by **15 litres** when the pressure is increased by 10 units at constant temperature.

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Would you like more details, or do you have any questions?

### Related Questions:
1. How will the volume change if the pressure is doubled instead?
2. What is the new volume if the pressure is decreased by 20 units?
3. How would the volume change if the temperature was not constant?
4. What is the percentage decrease in volume after the pressure increase?
5. If the initial volume was different, how would the solution change?

### Tip:
Remember that when variables are inversely proportional, their product remains constant.

Learn how to solve a gas law problem where the volume of a gas decreases with an increase in pressure while keeping temperature constant. Detailed step-by-step solution provided, covering inverse proportionality and gas law concepts. Suitable for Grades 9-12.

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