Question 4.P.12: If temperature does not change with height, estimate the boi...
If temperature does not change with height, estimate the boiling point of water at a height of 3000 m above sea-level. The barometer reading at sea-level is 98.4 kN/m² and the temperature is 288.7 K. The vapour pressure of water at 288.7 K is 1.77 kN/m². The effective molecular weight of air is 29 kg/kmol.
The air pressure at 3000 m is P_2 and the pressure at sea level, P_1=98.4 kN / m ^2.
\int v d P+\int g d z=0
v=v_1\left(P / P_1\right)
and: P_1 v_1 \int \frac{ d P}{P}+\int g d z=0
and: P_1 v_1 \ln \left(P_2 / P_1\right)+g\left(z_2-z_1\right)=0
v_1=(22.4 / 29)(288.7 / 273)(101.3 / 98.4)=0.841 m ^3 / kg.
∴ 98,400 \times 0.841 \ln \left(P_2 / 98.4\right)+9.81(3000-0)=0
and: P_2=68.95 kN / m ^2
The relationship between vapour pressure and temperature may be expressed as:
\log P=a+b T
When, T=288.7, P=1.77 kN / m ^2
and when, T=373, P=101.3 kN / m ^2
∴ \log P=-5.773+0.0209 T
When P_2=68.95, T=\underline{\underline{364 K }}.