A cylinder contains of oxygen (O2) 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
The mercury manometer shown in FIGURE P18.56 is attached
to a gas cell. The mercury height h is 120 mm when the cell is
placed in an ice-water mixture. The mercury height drops to
30 mm when the device is carried into an industrial freezer.
What is the freezer temperature?
Hint: The right tube of the manometer is much narrower than the
left tube. What reasonable assumption can you make about the gas
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