Calculation of true thickness of the bed

127. A newly discovered planet has an atmosphere made of a gas whose specific heat c_P is 1000 J Kg^-1 K^-1 .If the lapse rate is 20 K/km , what is its acceleration due to gravity?

A) 10 m/s²         

B) 20 m/s²           

C) 5 m/s²                 

D) 25 m/s²

Solution:

Formula:

$\frac{dT}{dz}=\frac{-g}{c_p}$---(1)

Adiabatic lapse rate $(-\frac{dT}{dz})$ = 20 K/km

g= gravitational acceleration 

$c_p$ = Specific Heat Capacity at Constant Pressure =1000 J Kg^-1 K^-1

From above eq (1),Acceleration due to gravity is given that,

$g =c_p*(-\frac{dT}{dz})$

$(-\frac{dT}{dz})=20 K/km =0.02K/m$

$g=0.02 *1000$

$g=20 m/s^2$

Joule= N m

$N=kg m /s^2$

Reference: http://lasp.colorado.edu/~bagenal/3720/CLASS14/14EVM-5.html