127. A newly discovered
planet has an atmosphere made of a gas whose specific heat cP 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
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