Q10 of 100 Page 34

The temperature and pressure at Shimla are 15.0°C and 72.0 cm of mercury and at Kalka these are 35.0°C and 76.0 cm of mercury. Find the ratio of air density at Kalka to the air density at Shimla.

We know ideal gas equation


PV=nRT


Where V= volume of gas


R=gas constant


T=temperature


n=number of moles of gas


P=pressure of gas


Number of moles n ==


Density


Given:


Temperature of Shimla T1=15.0°C


T(K)=T ()+273.15


T1=T(K)=15+273.15=288.15K


Pressure of Shimla P1 = 72.0 cm of mercury


Temperature of Kalka T2 = 35.0°C


T(K)=T ()+273.15


T2=T(K)=35+273.15=308.15K


Pressure of Kalka P2=76.0 cm of mercury


Substituting the value of n and in ideal gas equation, we get


=


So,





Taking the ratio of equations (i) and (ii),





The ratio of air density at Kalka to the air density at Shimla is 0.98.


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