Question

In physics, Boyle’s law states that if the temperature is constant, then the pressure, P, of a gas is inversely proportional to the volume, V, of the gas. If the pressure of the gas in a cylinder is equal to 250 kilopascals when the volume of the container is 1.7 cubic meters, then determine the constant of proportionality for this situation.

Answer 1

The constant of proportionality for this situation is 425

Step-by-step explanation:

When a quantity is inversely proportional with another quantity, then

the product of the two quantities is constant

1. If y is inversely proportional with x

2. Then y ∝ $\frac{1}{x}$

3. that mean y = $\frac{k}{x}$ where k is the constant of variation

4. Then xy = k

∵ In physics, Boyle’s law states that if the temperature is constant

∵ The pressure, P, of a gas is inversely proportional to the volume,

   V, of the gas

∴ P ∝ $\frac{1}{V}$

∴ P = $\frac{k}{V}$

∵ The pressure of the gas in a cylinder is equal to 250 kilo pascals

∵ The volume of the container is 1.7 cubic meters

- Substitute these values in the rule of variation to find k

∴ 250 = $\frac{k}{1.7}$

- Multiply both sides by 1.7

∴ k = 425

The constant of proportionality for this situation is 425

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