Simple Nature - Light and Matter

a symbols.kg · m21 J = 1= 1s 2kg · m2s 2= 10 7 g · cm2s 2= 10 7 erg× 1000 g ( ) 100 cm 21 kg × 1 mCabin air in a jet airplane example 3⊲ A jet airplane typically cruises at a velocity of 270 m/s. Outsideair is continuously pumped into the cabin, but must be cooled offfirst, both because (1) it heats up due to friction as it enters the engines,and (2) it is heated as a side-effect of being compressed tocabin pressure. Calculate the increase in temperature due to thefirst effect. The specific heat of dry air is about 1.0×10 3 J/kg·◦C.⊲ This is easiest to understand in the frame of reference of theplane, in which the air rushing into the engine is stopped, and itskinetic energy converted into heat. 6 Conservation of energy tellsus0 = ∆E= ∆K + ∆E heat .In the plane’s frame of reference, the air’s initial velocity is v i =270m/s, and its final velocity is zero, so the change in its kinetic energyis negative,∆K = K f − K i= 0 − (1/2)mv i2= −(1/2)mv i2.Assuming that the specific heat of air is roughly independent oftemperature (which is why the number was stated with the word“about”), we can substitute into 0 = ∆K + ∆E heat , giving0 = − 1 2 mv i 2 + mc∆T12 v i 2 = c∆T .Note how the mass cancels out. This is a big advantage of solvingproblems algebraically first, and waiting until the end to plug in6 It’s not at all obvious that the solution would work out in the earth’s frame ofreference, although Galilean relativity states that it doesn’t matter which framewe use. Chapter 3 discusses the relationship between conservation of energy andGalilean relativity.Section 2.1 Energy 79