A particular vehicle has an eight-cylinder engine. At the beginning of a compres

Question

A particular vehicle has an eight-cylinder engine. At the beginning of a compression stroke, each cylinder contains   640 cm3    of air (mixed with fuel) at atmospheric pressure and a temperature of   29.6 C   . A piston then rapidly compresses the air down to a volume of   60 cm3   . You may assume   =1.4 for the air and fuel mixture.

Part A-How many moles of air are enclosed by the piston?

Part B-What is the temperature of the gas after the compression?

Part C-What is the gauge pressure of the gas after it is compressed?

Part D-How much work was done by the gas during the compression?

Explanation / Answer

    Given
   volume (initial) of each cylinder is 640 cm^3 = 0.64 lt *8=5.12 lt---->v1

   v1= 5.12 lt, p1 = 1 atm , T1 = 29.6 0C = 302.6 k
      
        v2= 0.060 lt, p2 = ?,   T2 = ?, gamma = 1.4

from gas equation
Part A) PV= nRT ==> n= PV/RT = 1*5.12/ (0.0821*302.6)= 0.20609

Part B) relation between temperature and volume in adiabatic process is TV^-1 = constant

       T1v1^-1 = T2v2^-1

       T2 = T1(v1/V2)^-1

           = 302.6(5.12/0.060)^1.4-1
                   = 1791.91 K
           = 1518.76 0c
Part C) gauge pressure

       P1 =1 atm, P2 = ?

       PV^Y = constant ====> P1V1^Y = P2V2^Y
                   P2 = P1(V1/V2)^Y
                       = 1*(5.12/0.06)^1.4
                       = 505.31 atm
now gauge pressure is 505.31 - 1 = 504.31 atm

Part D) workdone by the gas during compression is

       W = P1V1 - P2V2/(Y-1)
          = (1*5.12 - 504.31*0.060) / (1.4 -1)
           = - 62.845 lt atm
   W = 6368 J
   

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