Posted by Justin on .
While taking a plane flight to a meeting, a physicist decides to do a mental calculation of how much fuel the plane would consume in the absence of friction, assuming its engines have an efficiency of 22.0% and the mass of the plane is 200,000 kg. Each gallon of jet fuel produces 1.30 multiplied by 108 J of heat when burned.
(a) How many gallons of fuel are used to get the plane from rest to the takeoff speed of 55.0 m/s?
(b) How many gallons to get to a cruising speed of 250 m/s and an altitude of 10.0 km?
(c) How much waste heat is produced in each case(in part a and b)? (Both the actual fuel consumption and heat produced will be greater because of air resistance.)
I know how to do the first one.
And part of (c)
Q waste=1.3*10^8*10.6-0.5*200000*55^2=1.08*10^9 J
=2•10⁵•55²/2•0.22•1.3•10⁸ =10.6 gal
0.22•N₂•Q= mv₂²/2 -mv₁²/2 +mgh,
N₂ = m(v₂² -v₁² +2gh)/2•0.22•Q=
=2•10⁵(250²- 55² +2•9.8•10⁴)/2•0.22•1.3•10⁸=
(c) Q₁ = N₁•Q=10.6•1.3•10⁸=1.37•10⁹ J
Waste Q₁ =0.78•1.37•10⁹=1.07•10⁹ J
Q₂=N₂•Q= 900.3•1.3•10⁸ =1.17•10¹¹ J
Waste Q₂= 0.78•1.17•10¹¹ = 9.13•10¹⁰ J