Respuesta :
Answer:
Joint variation states that:
If z is directly proportional to x and inversely proportional to y,
i.e, [tex]z \propto x[/tex] , [tex]z \propto \frac{1}{y}[/tex]
then the equation is in the form: [tex]z = k\frac{x}{y}[/tex] 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 [tex]V \propto T[/tex] , [tex]V \propto \frac{1}{P}[/tex]
by definition of joint variation:
[tex]V = k\frac{T}{P}[/tex] .....[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;
[tex]10 = k\frac{300}{1.5}[/tex]
Simplify:
[tex]10 = 200k[/tex]
Divide by 200 both sides we have;
[tex]k = \frac{10}{200} =\frac{1}{20}[/tex]
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;
[tex]V = \frac{1}{20} \cdot \frac{400}{5} = \frac{20}{5} = 4[/tex]
Therefore, the Volume of a gas is, 4 liters
