Question A 3.00 mol-sample of dry air occupying 2.00 times 10-1 m3 at 400 K is c

Question

Question

A 3.00 mol-sample of dry air occupying 2.00 times 10-1 m3 at 400 K is compressed in a sealed piston-cylinder assembly until its temperature reaches 2000 K and its volume is one-fifth its original volume. Assume dry air can be described as an ideal gas with a mean molar heat capacity at constant pressure of 29.0 J/mol-K. Determine the initial & final pressures (in Pa). Determine delta U(in kJ). Determine W & Q (in kJ) if the compression is performed irreversibly against a constant external pressure in a single step. Determine W & Q (in kJ) if instead the compression is performed reversibly along a path with PV2 = constant. Explain the difference in your answers for parts c & d.

Explanation / Answer

We know PV = nRT, using all in SI units.

a)

P1(2X10^-1) = 3(8.314)(400)

P1 = 49.884 kPa

P2(0.2/5) = 3(8.314)(2000)

P2 = 1247.1 kPa.

b)

Cv = Cp - R

Cv = 29.0-8.314 = 20.686

deltaU = 3(20.686)(2000-400)

= 99.29kJ

c)

W(single step) = P1(V2 - V1)

                          =49.884(0.2/5-0.2)

                         =-7.981 Kj

Q = U + W

= 99.29-7.981 = 91.309KJ

d)

W = (P2V2-P1V1)/1-K

      =-( (1241.1)(0.2/5) - ((49.884)(0.2))

                         =-39.66Kj

                       

Q = U + W

= 99.29-39.66 = 59.63KJ

e) There is a difference because the second process is reversible so it encounters a different pressure at each step and hence different work done.

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