Calculate the temperature of the air mass when it has risen to a level at which atmospheric pressure is only 8.00×104 pa . assume that air is an ideal gas, with γ=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:

Let's use the equation that relate the temperatures and volumes of an adiabatic process in a ideal gas.

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Now, let's use the ideal gas equation to the initial and the final state:

Let's recall that the term nR is a constant. That is why we can match these equations.  

We can find a relation between the volumes of the initial and the final state.

Combining this equation with the first equation we have:

Now, we just need to solve this equation for T₂.

Let's assume the initial temperature and pressure as 25 °C = 298 K and 1 atm = 1.01 * 10⁵ Pa, in a normal conditions.

Here,

Finally, T2 will be:

diagram is missing, but i will try to explain your doubt.

answer:

amplitude is the maximum displacement or distance moved on a point of a vibrating body or wave measured from its equilibrium position.it is equal to half the length of vibration path.

0.11 m/s and 0.28 m/s should be correct