A container, in the shape of a rectangle prism with dimensions l,w and h, is filled with an ideal gas and sealed. The average force exerted by the gas molecules on the bottom of the container is F. There are n moles of gas in the container and the temperature of the gas is T. What is h, the height of the container?

Question:

A container, in the shape of a rectangle prism with dimensions , and , is filled with an ideal gas and sealed. The average force exerted by the gas molecules on the bottom of the container is . There are moles of gas in the container and the temperature of the gas is . What is , the height of the container?

Answer:

Here, the volume of the gas is equal to the volume of the container. So write the equation of the volume of the gas.

  ......(1)

Write the equation of the area of the bottom of the container.

 ......(2)

The ideal gas law equation is,

Here, is the pressure of the ideal gas, is the volume of the ideal gas, is the number of the moles of the ideal gas, is the universal gas constant and is the temperature of the ideal gas.

According to definition of the pressure, write the equation of the pressure in terms of and .

 ......(3)

From the above equation (1), (2), (3) and the ideal gas law equation.