A room is heated up from t1=15C to t2=27C. The number of air molecules changed with how many percents?
The relation between the density, pressure and the temperarature of air is given by :
d= density of the gas, P is the pressure , R is the gas constant and T is the absolute temperature of the gas.
Applying the Law for the 2 situtions of temperatures, T1 and T2, the pressure remaing the same,
d1= (n)P/(R*T1) (1),
From (1) and (2):
(2)/(1) gets us:
d2/d1 = T1/T2
=96.00199 % of the earlier density, or, a reduction of 3.998001%.
The moles number could be calculated in 3 different manners:
The equation of state is:
p*V=(m/miu)*R*T=(N/NA)*R*T=(V/Vmiu)*R*T=N*k*T, where k is Boltzman's constant, k=R/NA.
The requested ratio is:
The number of molecules is decreasing with 4 percents.