Calculating temperature and pressure

In summary, the ideal gas law is a mathematical equation that relates the pressure, volume, temperature, and number of moles of an ideal gas. It is commonly written as PV = nRT and can be used to calculate temperature or pressure depending on the given information. Temperature is typically measured in Kelvin or degrees Celsius, while pressure can be measured in atmospheres, millimeters of mercury, or kilopascals. According to the ideal gas law, as temperature increases, the pressure of a gas also increases, and when the volume of a gas is decreased, the pressure increases. Additionally, as the number of moles of a gas increases, both the temperature and pressure also increase.
  • #1
striphe
125
1
A 100 Km long tube of ideal gas (molecular mass equivalent to argon) is perfectly insulated from the outside environment. At the bottom of this tube, it is 20C with a pressure of 100 KPa. This tube is affected by the same 10 m/s^2 gravitational acceleration throughout.

I have no idea of how to calculate what the pressure and temperature is at the top of this long tube. Can anyone offer a formula and work out a solution based on the variables given?
 
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  • #2
I am not 100% sure, but perhaps this will help.
 
  • #3
thanks Borek
 

What is the ideal gas law and how is it used to calculate temperature and pressure?

The ideal gas law, also known as the universal gas law, is a mathematical equation that describes the relationship between the pressure, volume, temperature, and number of moles of an ideal gas. It is written as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. This equation can be rearranged to calculate temperature or pressure, depending on the given information.

What are the units of temperature and pressure used in gas calculations?

Temperature is typically measured in Kelvin (K) or degrees Celsius (°C) in gas calculations. Pressure can be measured in various units, but the most common ones are atmospheres (atm), millimeters of mercury (mmHg), and kilopascals (kPa). It is important to make sure that all units are consistent in the calculation to ensure accurate results.

How does temperature affect the pressure of a gas?

According to the ideal gas law, as temperature increases, the pressure of a gas also increases, assuming that the volume and number of moles remain constant. This is because as the temperature of a gas increases, the average kinetic energy of its molecules also increases, causing them to collide with the walls of the container more frequently and with greater force, resulting in an increase in pressure.

What happens to the pressure of a gas when volume is decreased?

When the volume of a gas is decreased, the pressure increases, assuming that the temperature and number of moles remain constant. This is because as the volume decreases, the molecules of the gas become more crowded and collide with the walls of the container more frequently, resulting in a higher pressure.

How does the number of moles of a gas affect its temperature and pressure?

According to the ideal gas law, as the number of moles of a gas increases, the temperature and pressure also increase, assuming that the volume remains constant. This is because as more molecules are added to a fixed volume, there are more collisions with the walls of the container, resulting in an increase in both temperature and pressure.

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