One cylinder in the diesel engine of a truck has an initial volume of 700 cm3 .

Question

One cylinder in the diesel engine of a truck has an initial volume of 700 cm3 . Air is admitted to the cylinder at 30 C and a pressure of 1.0 atm. The piston rod then does 400 J of work to rapidly compress the air.

Part A

What is its final temperature?

Express your answer to two significant figures and include the appropriate units.

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Part B

What is its final volume?

Express your answer to two significant figures and include the appropriate units.

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One cylinder in the diesel engine of a truck has an initial volume of 700 cm3 . Air is admitted to the cylinder at 30 C and a pressure of 1.0 atm. The piston rod then does 400 J of work to rapidly compress the air.

Part A

What is its final temperature?

Express your answer to two significant figures and include the appropriate units.

Tfinal =

SubmitMy AnswersGive Up

Part B

What is its final volume?

Express your answer to two significant figures and include the appropriate units.

Vfinal =

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Explanation / Answer

Q = 0 J

delta S = 0 J / K

(P)(V)^k = Constant

(T)(V)^k - 1 = Constant

k = specific heat ratio = Cp / Cv = 1.4

V1 = ( 700 cm^3 ) ( 1 L / 1000 cu cm ) = 0.700 L

m = (P1)(V1)(M) / (R)(T1)

m = ( 1.000 atm )( 0.700 L)(28.96 g/gmol) / ( 0.08205 atm -L / gmol - K ) ( 303 K )

m = 0.815 g

WB = - 400 J

Q = delta U + WB

Since adiabatic: Q = 0.0 J

delta U = - ( WB ) = - ( - 400 J ) = 400 J

T2 - T1 = (delta U) / (Cv)(m)

T2 - T1 = ( 400 ) / (0.718 J / g-C-deg ) (0.815 g) = 683.56 C deg

T2 = T1 + ( T2 - T1 )

T2 = 30 C + ( 683.56 C deg ) = 713.56 C = 986.56 K

(T2)(V2)^k -1 = (T1)(V2)^k -1

V2 = (V1)(T1 / T2 )^1/k -1

V2 = ( 700 cm^3 ) ( 303 K / 986.56 K )^1/(1.4 - 1)

V2 = 36.6 ccm^3

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