Answer:
Final velocity = 119.83 m/s
Final elevation = 731.9 m
Explanation:
We are told that temperature of air changes from 0 to 10°C
Thus;
Change in temperature; ΔT = 10 - 0 = 10°C
Also, its velocity changes from zero to a final velocity. Thus;
v1 = 0 m/s
v2 is unknown
Also, its elevation changes from zero to a final elevation.
So, z1 = 0 and z2 is unknown
Now, we want to find v2 and z2 when the internal, kinetic and potential energy are equal.
Thus Equating the formula for both kinetic and internal energy gives;
½m(v2² - v1²) = mc_v•ΔT
m will cancel out and v1 is zero to give;
v2² = 2c_v•ΔT
v2 = √(2c_v•ΔT)
Where c_v is specific heat of constant volume of air with a constant value of 718 J/Kg.K
Thus;
v2 = √(2 × 718 × 10)
v2 = √14360
v2 = 119.83 m/s
To find z2, we will equate potential energy formula to that of the internal energy.
Thus;
mg(z2 - z1) = mc_v•ΔT
m will cancel out and since z1 is zero, then we have;
z2 = (c_v•ΔT)/g
z2 = 718 × 10/9.81
z2 = 731.9 m
