On a warm summer day, a large mass of air (atmospheric pressure 1.01×105Pa ) is
ID: 1515600 • Letter: O
Question
On a warm summer day, a large mass of air (atmospheric pressure 1.01×105Pa ) is heated by the ground to a temperature of 25.0 C and then begins to rise through the cooler surrounding air.
1- Calculate the temperature of the air mass when it has risen to a level at which atmospheric pressure is only 8.20×104 Pa . Assume that air is an ideal gas, with =1.40 . (This rate of cooling for dry, rising air, corresponding to roughly 1 C per 100 m of altitude, is called the dry adiabatic lapse rate.)
Explanation / Answer
P1 = 1.01*10^5 Pa, P2 =8.2*10^4 Pa, T1 =25 oC =25+273 = 298 K
=1.40
for adiabatic process P^1- *T^= constant
P1^1- *T1^ = P2^1- *T2^
(1.01*10^5)^-0.4 *(298)^1.4 = (8.2*10^4)^-0.4* T2^1.4
T2 =280.8 K
T2 =280.8 --273 = 7.8 oC