Question

One cylinder in the diesel engine of a truck has an initial volume of 700 cm3 . Air is admitted to the cylinder at 35 ∘C and a pressure of 1.0 atm. The piston rod then does 500 J of work to rapidly compress the air. What is its final temperature? What is its final volume?

Answer 1

Sol::

Given data:

initial volume of 700 cm³
Temperature 35 ∘C
and a pressure of 1.0 atm.
Work 500 J

Here The compression step is treated as adiabatic and reversible ( isentropic )

So
Q = 0.0 J and Δ S = 0.0 J / K

P* ( V )^k = Constant

T *( V )^k - 1.0 = Constant

k = specific heat ratio
= Cp / Cv
= 1.400

V1 = ( 700) ( 1 L / 1000 )
= 0.7000 L

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

m = (1) ( 0.7 ) ( 28.96) / ( 0.08205 )( 308.15 )
= 0.8018 g

WB = - 500 J

Q = ΔU + WB

Since adiabatic: Q = 0.0 J

ΔU = - ( WB )
= - ( - 500 J )
= 500 J

Now
T2 - T1 = ( ΔU ) / ( Cv*m )
= ( 500 ) / ( 0.718) ( 0.8018)
= 868.52° C

T2 = T1 + ( T2 - T1 )

T2 = 35° + ( 868.52° )
= 903.52° C
= 1176.67 K

B)

T2*( V2 )^k -1.0 = T1*( V1 )^k -1.0

V2 = V1 * ( T1 / T2 )^1/k -1.0

V2 = ( 700) ( 308.15 / 1176.67 )^1/1.4 - 1.0

V2 = 24.56 cm³

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