# A room is heated up from t1=15C to t2=27C. The number of air molecules changed with how many percents?

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The relation between the density, pressure and the temperarature of air is given by :

d=(n)P/(R*T),where

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),

d2=(n)P/(R*T2) (2).

From (1) and (2):

(2)/(1) gets us:

d2/d1 = T1/T2

= ((273.15+15)/(273.15+27)

=288.15/300.15

=0.96001999

=96.00199 % of the earlier density, or, a reduction of 3.998001%.

The moles number could be calculated in 3 different manners:

niu=m/miu=N/NA=V/Vmiu

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:

##### (N2-N1)/N1=[pV/kT2-pV/kT1]/(pV/kT1)=(T1-T2)/T2=-4.0%

The number of molecules is decreasing with 4 percents.