hence : ^ . ^ 4 ^f .,,
v=zv (l +at). °
If the temperature of a gas be raised without allowing it to expand, the pressure increases according to the formula :
JP=i>o( 1 +"t).
By combining these two equations we get the General Equation of a Gas :
This equation can be arrived at directly from the following considerations. Let v be the volume of a gaseous mass at 0° and under the normal pressure p (76 centi- metres of mercury), then the volume at t° under the same pressure will be v (1 + at). Let the pressure be now reduced to 1 centimetre of mercury, then the volume will increase to v (1 + a t)p , and if the gas be now compressed to the pressure p the final volume will be
v __ p Vo(l+at) V or p v = p v (1 + a t).
Transformation of the General Equation : pv=zp v (l + at).
At £°,the absolute temperature (counting from —278° C.)
will be
t = 273 + t.
Therefore
t = t - 273.
��1 % Z ?ZT } at *» temperature U p B = normal atmospheric pressure = 760 millimetres of mer- cury. v 9 = volume at 0° under normal pressure.
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