problem20_53

# University Physics with Modern Physics with Mastering Physics (11th Edition)

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20.53: (Extra figures are given in the numerical answers for clarity.) a) The efficiency is 611 . 0 1 40 . 0 = - = - r e , so the work done is J. 78 | | and J 122 C = = Q e Q H b) Denote the length of the cylinder when the piston is at point a by 0 L and the stroke as s . Then, is volume and , 1 0 0 0 s L r r r s L L - - = = . m 10 0 . 51 ) m 10 25 . 41 ( ) m 10 4 . 86 ( 6 . 9 6 . 10 1 3 4 2 3 3 0 - - - × = × × = - = π sA r r A L c) The calculations are presented symbolically, with numerical values substituted at the end. At point a , the pressure is 3 4 4 m 10 10 . 5 is volume the Pa, 10 50 . 8 - × = × = a a V p as found in part (b) and the temperature is , is volume the , point At K. 300 r V V b T a b a = = the pressure after the adiabatic compression is γ a b r p p = and the temperature is 1 - = γ a b r T T . During the burning of the fuel, from , to c b the volume remains constant and so . r V V V a b c = = The temperature has changed by an amount ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 , K mol J 5 . 20 m 10 10 . 5 Pa 10 50 . 8 J 200 K mol J 3145 . 8 3 4 4 H H H a a a V a a V a a a V T f T T C V p RQ C RT V p Q nC Q T = × × = = = = - where f is a dimensionless constant equal to 1.871 to four figures. The temperature at c is then ( 29 f r T T f T T γ a a b c + = + = - 1 . The pressure is found from the volume and temperature, ( 29 f r r p p γ a c + = - 1 . Similarly, the temperature at point d is found by

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