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# Charles's Law

Extracts from this document...

Introduction

## However, if the walls are flexible, as the temperature increases the volume increases to maintain even pressure. This is called Charles’s Law.

Charles law states that the volume of a given amount of dry ideal gas is directly propotional to the Kelvin Temperature, provided the amount of gas and the pressure remains fixed.i.e.

V=constant ( t + 273.15)
Where t is the gas temperature on Celsius scale.

There are interesting points regarding the relationship between volume and temperature changes.

-273ºCT (ºC)

Since gases expand and contract at a constant rate, extrapolation of this behavior shows that the effective volume goes to zero around -273 ºC.

Middle

Charles's Law

or

=const.
T

or

## = T1T2

Charles's law is a special case of the perfect gas equation andconcludes that the volume of any gas should extrapolate to zero at t = - 273.15 C. This law may be stated as following equation:

V=constant T                                         where T is the absolute temperature.

## diagram

Conclusion

Rearranged as: a = F
m
showing that acceleration is indirectly proportional to the mass if the force releasing the ball bearing remains constant. Therefore, if the mass is increased, the acceleration of the ball bearing will be decreased during its trajectory.

Theory for horizontal motion:

Loss of PE = Gain of PE

mgh = ½ mv2

2mgh = v2
m

v = Ö(2gh)

It is range we are trying to find out:

s = ½ (u+v) t = ut = vt

R = Ö(2gh) = Ö(2H/g) (from equation: ‘time of flight´)

R = Ö(4hH)

R2 = 4hH

From this derived equation a testable hypothesis can now be made. By comparing the derived formula with the formula for a straight line graph, which shows similar properties, it is thought that as height increases, range will also increase.

R2 = 4 x h x H

R2 = (4 x h) x H + 0

y = m x + c

This comparison of equations shows that if Range2 were plotted against height (h) then a straight line graph through the origin would be the result. It can therefore be said that Range2 is directly proportional to height, considering that height (H) is constant. The mass and size of the ball bearing must also be kept constant. To prove this, a graph of Range2 on the y-axis and height (h) on the x-axis must be plotted and a straight line graph running through the origin must be produced from the data. This would show the theory and equations used to be correct.

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