# 1: For a given amount, type, and temperature of gas, when its pressure is increased from 200 kPa to 500 kPa, what will its volume be if its initial volume is 3 cubic meters?

Mar 20, 2018

${\text{1.2 m}}^{3}$

#### Explanation:

$P \cdot V = n \cdot R \cdot T \text{ }$(Ideal gas law)

Assuming that the amount of gas and the temperature are fixed, the product of the pressure and volume is constant at any given moment. Using this, you can find the simple equation:

For ${P}_{1}$ and ${V}_{1}$ as the initial pressure and volume and ${P}_{2}$ and ${V}_{2}$ as the pressure and volume at any given moment.

${P}_{1} \times {V}_{1} = {P}_{2} \times {V}_{2}$

Writing the values, we get:

$\text{3 m"^3 xx "200 kPa" = V_2 xx "500 kPa}$

So

$\text{600 kPa m"^3 = V_2 xx "500 kPa}$

${V}_{2} = {\text{600 kPa m"^3/"500 kPa" = 6/5 quad "m"^3 = "1.2 m}}^{3}$

Since we only played with numbers, the volume is still as cubic meters.