problem20_63

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

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20.63: a) For an ideal gas, , R C C V P + = and taking air to be diatomic, . and , 5 7 2 5 2 7 = = = γ R C R C V P Referring to Fig. (20.6), ). ( ) ( 2 7 2 7 H b b c c b c V p V p T T R n Q - = - = Similarly, ). ( 2 5 C d d a a V p V p R n Q - = What needs to be done is to find the relations between the product of the pressure and the volume at the four points. For an ideal gas, , b b b c c c T V p T V p = so ( 29 . a c T T a a c c V p V p = For a compression ratio r , and given that for the Diesel cycle the process ab is adiabatic, . 1 1 - - = = γ a a γ b a a a b b r V p V V V p V p Similarly, . 1 - γ = a c c c d d V V V p V p Note that the last result uses the fact that process da is isochoric, and b c a d p p V V = = also, ; (process bc is isobaric), and so ( 29 . a c T T b c V V = Then, γ - - - = = = = r T T V V V T V T T T V V T T T T V V T T V V a c γ b a
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Unformatted text preview: a a a c b a b a a b a b b c a c 1 1 Combining the above results, 2 γ γ a c a a d d r T T V p V p-γ = Subsitution of the above results into Eq. (20.4) gives ( 29 - --=--1 2 1 7 5 1 γ r r a c γ T T T T e a c , ) 167 . 3 ( 1 ) 002 . 5 ( 4 . 1 1 1 40 . 56 . ---=-r r where 4 . 1 , 167 . 3 = γ = a c T T have been used. Substitution of . 21 = r yields %. 8 . 70 708 . = = e...
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