The volume v of a gas varies inversely as the pressure p and directly as the temperature a certain gas has a volume of 10 liters (l), a temperature of 300 kelvins (k), and a pressure of 1.5 atmospheres (atm). if a gas has a temperature of 400 kelvins and a pressure of 5 atmospheres; what is its volume?

Joint variation states that:

If z is directly proportional to x and inversely proportional to y,

i.e, ,

then the equation is in the form: where k is the constant of variation.

From the given information: The volume V of a gas varies inversely as the pressure P and directly as the temperature

i.,e ,

by definition of joint variation:

 .....[1] where k is the constant of variation.

It is also given that a certain gas has a volume of 10 liters(L) , a temperature of 300 kelvins(K), and a pressure of 1.5 atmosphere(atm).

Substitute these given values in [1] to solve for k;

Simplify:

Divide by 200 both sides we have;

Now, if a gas has a temperature of 400 kelvins and a pressure of 5 atm.

To find the volume (V);

Now substitute the given data and value of k in [1] we have;

Therefore, the Volume of a gas is, 4 liters