Question 46

Expert-verifiedFound in: Page 512

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

A cylinder contains of oxygen (O_{2}) at a pressure less than . The cap on one end of the cylinder is held in place only by the pressure of the air. One day when the atmospheric pressure is , it takes a force to pull the cap off. What is the temperature of the gas?

The temperature of the gas is

Given : A -diameter, -long cylinder contains of oxygen at a pressure less than . When atmospheric pressure is , it takes a force to pull the cap off.

The ideal gas law () relates the macroscopic properties of ideal gases.

Since the pressure comes from inside the gas, we can apply the ideal gas law to find an expression for the temperature

Knowing that we are giving the mass and not the number of moles, we can rewrite the previous formula as follows., where is the molar mass of the gas inside and is the mass of that gas.

Based on __Newton's first law__ and the definition of pressure, we can write for the cap that

Where is the internal pressure, is the atmospheric pressure,

is the area of the cap and is the force we have to apply to move the cap.We can now substitute the expression we found for pressure into our result for temperature:

Remembering that for a cylinder , we can further simplify to If we apply our numerical input data, we find the value for the temperature inside as follows.

Inserting the values, we get

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