A system consists of an ideal gas with Cv,m= 20.86 J mol^-1K^-1 (constant over t

Question

A system consists of an ideal gas with Cv,m= 20.86 J mol^-1K^-1 (constant over the temperatures of interest). The gas is initially at temperature 250.0 K, volume 3.000 L, and pressure 1.500 bar. For each of the following processes, calculate the final values of T, P, V, q, w, DeltaU, and deltaH. Show your work and make a table of the results. The initial state of the system is the same for each part (they aren't done sequentially). (a) Constant volume heating to a final temperature of 450.0 K. (c) Constant pressure heating to a final temperature of 450.0K, with the gas expanding against an external pressure of 1.500 bar. (c) Heating to a final temperature of 450.0 K and volume of 3.500 L against an external pressure of 1.000 bar. (d) Reversible isothermal expansion to a final pressure of 1.000 bar. (e) Adiabatic expansion against an external pressure of 1.000 bar to a final volume of 4.000 L.

Explanation / Answer

There are muliple questions here for each part I need to calculate 7 values. So in total 35 parts. I will solve 1st question for you.

a)
Final temperature, T = 450 K
Since V is constant,
final Volume = 3 L
Work done = -P * (delta V)
since delta V = 0
Work done, W = 0

delta U = n*Cv* delta T
    = 1* (20.86) * (450-250)
    = 4172 J

delta U =q+ W
since W is 0
q = delta U
   =   4172 J

final P = Initial P * Tf /Ti
          = 1.5*450/250
           = 2.7 bar
delta (P*V) = (2.7*3 - 1.5*3)
    = 3.6 bar L
     = 360 J {Since 1 barL = 100 J}
   delta H = delta U + delta (P*V)
    = 4172 + 360
     = 4532 J

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