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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 much will its volume decrease?.

To solve this problem, we'll use the fact that, at constant temperature, the pressure \(P\) of a gas is inversely proportional to its volume \(V\). This relationship can be expressed as:

\[
P \cdot V = k
\]

where \(k\) is a constant.

### Step-by-Step Solution

1. **Find the constant \(k\):**

   Given:
   - Initial volume, \(V_1 = 1140\) liters
   - Initial pressure, \(P_1 = 750\) units

   The product \(P_1 \cdot V_1 = k\), so:

   \[
   k = 750 \times 1140
   \]

2. **Determine the new pressure \(P_2\):**

   The pressure is increased by 10 units, so:

   \[
   P_2 = P_1 + 10 = 750 + 10 = 760 \text{ units}
   \]

3. **Find the new volume \(V_2\):**

   Since the product \(P \cdot V\) remains constant, we have:

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

   Substituting the values:

   \[
   750 \times 1140 = 760 \times V_2
   \]

   Solving for \(V_2\):

   \[
   V_2 = \frac{750 \times 1140}{760}
   \]

4. **Calculate the decrease in volume:**

   The decrease in volume, \(\Delta V = V_1 - V_2\).

Now, let's compute these values.The new volume of the gas, after the pressure is increased by 10 units, is \(1125\) liters. 

The decrease in volume is \(15\) liters.

### Summary:
- **New Volume (V₂):** 1125 liters
- **Decrease in Volume:** 15 liters

Would you like more details or have any questions?

### Related Questions:
1. How is the relationship between pressure and volume described in the ideal gas law?
2. What would happen to the volume if the pressure was decreased by 10 units instead?
3. How does temperature affect the relationship between pressure and volume in a gas?
4. What other factors can influence the pressure of a gas in a closed container?
5. How can Boyle's Law be applied to solve problems involving changes in gas conditions?

**Tip:** Always remember that for gases at a constant temperature, the pressure and volume are inversely related!

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 much will its volume decrease?

Learn how to calculate the decrease in the volume of gas when pressure increases using Boyle's Law. This example demonstrates how pressure and volume are inversely related, with a detailed step-by-step solution. Suitable for students in Grades 10-12.

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