Question

... CALC Earth’s Atmosphere. In the troposphere,the part of the atmosphere that extends from earth’s surface to an altitude of about The temperature is not uniform but decreases with increasing elevation. (a) Show that if the temperature variation is approximated by the linear relationship where is thetemperature at the earth’s surface and Tis the temperature at height y, the pressure pat height yis ln a

where is the pressure at the earth’s surface and Mis the molar mass for air. The coefficient a is called the lapse rate of temperature. It varies with atmospheric conditions, but an average value is about . (b) Show that the above result reduces to the result of Example 18.4 (Section 18.1) in the limit that (c) With calculate pfor and compare your answer to the result of Example 18.4. Take and .

Short answer

(a)Relation of pressure by variation oftemperatureis

(B)The above result reduces to the result of Example 18.4 (Section 18.1) in the limitis

(c),the pressure is and accuracy is

Step-by-step solution

About Lapse rate of temperature And Determine relation of pressure by variation of temperature

The lapse rate is the rate at which an atmospheric variable, normally temperature in Earth's atmosphere, falls with altitude

Solve forrelationof pressure

Evaluate change inpressurewith respect to y

Integrateboth side with respect to pressure

Therefore ,relation of pressure by variation of temperature is

Determine the above result reduces to the result of Example 18.4 (Section 18.1) in the limit 

The pressure is

For

Take exponential for both side

Therefore the above result reduces to the result of Example 18.4 (Section 18.1) in the limitis .

Determine the pressure

Therefore ,the pressure is and accuracy is