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Solution 3 - Physics 2C Summer Session I Quiz#3 1 The speed...

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Physics 2C Summer Session I Quiz #3 1. The speed of sound is given by v s = p °P=±: From the ideal gas law the molar density is n=V = P=RT: Hence the mass density on Titan is ± = nm mol =V = m mol 3 P RT = : 028 3 1 : 01 ° 10 5 8 : 314 ° 293 ± = : 387 kg=m 3 (ideal gas law). For a pressure of P = 1 : 5 ° 10 5 Pa the speed of sound is v s = p 1 : 4 ° 1 : 5 ° 10 5 =: 387 = 737 m= sec ( B ) 2. The decibel level is de°ned as ² = 10 log ( I=I o ) : Hence ² 2 ± ² 1 = 10 log ( I 2 =I 1 ) = ± 12 I 2 =I 1 = 10 ° 1 : 2 = : 0631 or I 1 =I 2 = 16 ( E ) 3. In a Carnot cycle the net work is done during the isothermal processes. For this Carnot cycle that is W = (( PV ) h ± ( PV ) c ) ln 2 W = (800 ± 661) ln 2 = 96 : 4 J The e¢ ciency is given by e = W Q h = 96 : 4 800 ln 2 = 17% ( A ) 4. The maximum and minimum temperatures can be found from the ideal gas law, T h = ( PV ) h nR = 800 : 2 ° 8 : 314 = 481 K T c = ( PV ) c nR = 661 : 2 ° 8 : 314 = 397 : 5 K The Carnot e¢ ciency is given by e = Q h ± Q c Q h = 1 ± T c T h = 1 ± 397 : 5 481 = 17% ( E ) 1
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5. The COP is de°ned as COP = Q c W : Since Q c = mL f = : 9 kg (334 kJ=kg ) = 301 kJ; the work done is W = Q c COP = 301 5 : 2 = 58 kJ ( B ) : 6.
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