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## Homework Statement

An air parcel is investigated to study the weather.It rises up and rests at an equilibrium height in the atmosphere,where its weight is exactly balanced by the upward buoyant force. We shall assume

ideal gas law to hold for all processes and neglect the mass of the air parcel. If the air parcel is displaced vertically, it is often found to oscillate about the equilibrium position. The frequency of this oscillation is called “Brunt-Vais¨al¨a” frequency. Now suppose the air parcel is displaced upwards adiabatically from the equilibrium

position. Let M(b) and M(a)be the molar mass of the air parcel and the atmosphere respectively.and C(b) and C(a) be the molar heat capacity at constant volume for the air parcel and the atmosphere respectively .

Find the equilibrium height of the air parcel.

Hints:First find the lapse rate for both the air parcel and the atmosphere. Then find out the acceleration of the air parcel.

2. Homework Equations :

2. Homework Equations :

I first find the lapse rate ,Γ=dT/dz for both of them. And it is

Γ(a)=-M(a)g/C(a) and

Γ(b)=-M(a)gT(b)/C(b)T(a)

And z''=g((M(a)T(b)/M(b)T(a))-1)

But i couldn't find out equilibrium height equating z" to zero. Please help me to find this.

(The original problem (1st one) is posted here)

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