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The pressure, P, of a gas varies inversely with its volume, V. Pressure is measured in units of Pa. Suppose that a particular amount of a gas is initially at a pressure of 84 Pa at a volume of 51 L. If the volume is expanded to 153 L, what will the new pressure be?

Verified Answer :

alex3245

P = k/V

84 = k/51
4,284 = k

P = 4,284 / 153
P = 28Pa

Hope I helped!

Answer:

Inverse variation states:

If \(y \propto \frac{1}{x}\)

then the equation is in the form of :

\(y = \frac{k}{x}\)

where, k is the constant of variation.

As per the statement:

The pressure, P, of a gas varies inversely with its volume, V

By inverse variation definition;

\(P= \frac{k}{V}\)            ....[1]

It is also given that  a particular amount of a gas is initially at a pressure of 84 Pa at a volume of 51 L

⇒P = 84 Pa and V = 51 L

then;

\(84= \frac{k}{51}\)

⇒\(k=84 \cdot 51=4284\)

If the volume(V) is expanded to 153 L then find the new pressure.

Using [1] we have;

\(P= \frac{4284}{153} =28\) Pa

Therefore, the new pressure be , 128 Pa

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