Question

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?

Answer 1

Answer:

Joint variation states that:

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

i.e, $z \propto x$ , $z \propto \frac{1}{y}$

then the equation is in the form: $z = k\frac{x}{y}$ 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 $V \propto T$ , $V \propto \frac{1}{P}$

by definition of joint variation:

$V = k\frac{T}{P}$  .....[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;

$10 = k\frac{300}{1.5}$

Simplify:

$10 = 200k$

Divide by 200 both sides we have;

$k = \frac{10}{200} =\frac{1}{20}$

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;

$V = \frac{1}{20} \cdot \frac{400}{5} = \frac{20}{5} = 4$

Therefore, the Volume of a gas is, 4 liters