Why Does Gas Volume Decrease with Temperature Increase in My Calculations?

[CathyLou]

As part of my AS Physics homework a week or so ago, I was set the question:

3. A fixed mass of gas has a volume of 144 cm3 at 15ºC. Calculate its volume at

(a) 33ºC
(b) 0ºC, and
(c) -67ºC (the pressure being constant).

Yesterday the whole class was asked to re-attempt questiosn 3 and 4 using temperatures in Kelvin instead of Celcius.

When I was trying to figure out the question the first time around I tried using K but found that the answers didn't make logical sense as I thought that as temperature increases so does the volume of gas.

Originally, I used V = kT and calculated k to be 9.6. I the got the three answers to equal 317, 0 and -643 cm^3. Obviously, I now know that this is wrong.

However, whenever I try to calculate the answer using a temp. in Kelvin (by adding 273 degrees to the celcius temp), I get k to equal 0.5 and this figure makes the volume decrease as temp. increases.

Can anyone please tell me what I'm doing wrong?

Cathy

 

[Astronuc]

Start with PV=nRT=NkT, which is the ideal gas law. Note there are three variables, P, V and T. P and T must be used in terms of their absolute values. P can be expressed as absolute, gage or differential pressure, and T can be expressed in terms of absolute scales (Kelvin or Rankine) or corresponding relative scales, Celsius and Fahrenheit.

In addition, the units must be consistent, MKS (SI) or cgs, or British.

See http://hyperphysics.phy-astr.gsu.edu/Hbase/kinetic/idegas.html for a discussion of the ideal gas law.

A reasonable discussion of temperature - http://en.wikipedia.org/wiki/Thermodynamic_temperature

 

[CathyLou]

Thank you for replying.

As far as PV = nRT is concerned, how do I work out the number of moles so that I only have one unknown in the equation?

 

[Astronuc]

n = number of moles

So n = PV/RT.

R = universal gas constant = 8.3145 J/mol K

Otherwise, using 144 cm[subp]3[/sup] at 15ºC, and the fact that one mole of an ideal gas occupies 22.4 l = 22400 ml = 22400 cc at STP (273.15 K, 1 atm)

http://hyperphysics.phy-astr.gsu.edu/Hbase/kinetic/idegas.html#c4