Question

boyles law states that if the temperature and amount of gas remain unchanged, then the gas pressure exerted varies inversely to the volume that the gas occupies. suppose that buster the clowns helium tank has a volume of 3 liters, and the helium inside the tank is under the pressure of 40 kpa (kilopascal).
a) write an equation that relates the pressure in the helium tank to the volume of the tank. you may define your own single - letter variables.
b) if the helium in busters tank is transferred to an empty tank that has a volume of 17 liters and is the same temperature, what is the pressure exerted in the new tank? round your answer to 3 decimal places.

Explanation:

Step1: Define variables and use Boyle's law

Let \( P\) be the pressure and \( V\) be the volume. Boyle's law is \( P=\frac{k}{V}\) (where \( k\) is a constant). Given \( V = 3\) liters and \( P=40\) kPa, we substitute into the equation: \( 40=\frac{k}{3}\).

Step2: Solve for \( k\)

Multiply both sides by \( 3\): \( k = 40\times3=120\). So the equation is \( P=\frac{120}{V}\).

Step3: Find the pressure for \( V = 17\) liters

Substitute \( V = 17\) into \( P=\frac{120}{V}\): \( P=\frac{120}{17}\approx7.059\) kPa.

Answer:

a) The equation is \( P=\frac{120}{V}\).
b) The pressure is approximately \( 7.059\) kPa.