4. Calculate the total change in work, w, and internal energy, AE, for each of t

Question

4. Calculate the total change in work, w, and internal energy, AE, for each of the following processes For your answers enumerate the results for q, w, and E for each step. 5.00L of air expands to 20.0L by heating it from 300 K to 1200 K at a constant pressure of 3.00 atm. The heat required for this process is 17.8 kJ. (a) (b) 5.00 L of air initially at 3.00 atm is heated from 300 K to 1200 K while its volume is held constant. The heat required for this process is 12.8 kJ. Page 2 (c) The hot gas from part (b) is allowed to expand isothermally (constant temp.) until its pressure drops to 3.00 atm and its volume reaches 20.0 L. The heat required in this step is 9.7 kJ. Hint: Energy is a state function! Find a relationship among the pathways a,b, and c! ]

Explanation / Answer

(a) W = - p * (V2 - V1)
1 atm = 1.01325*105 Pa ; p = 3 *1.01325*105 = 303975 Pa
V1 = 5L = 0.005m3 ; V2 = 0.02m3
W = - 303975*(0.02-0.005) = -4559.625J = -4.5596 kJ
EA = W + q = -4.5596 kJ + 17.8 kJ = 13.2404 kJ

(b) Volume is constant so W will be zero
W = PV = 0 kJ ; q = 12.8kJ
  EB = W + q = 0 + 12.8 = 12.8 kJ

(c) Energy is a state fuction so, EA = EB + EC
EC = 13.2404 kJ - 12.8 kJ = 0.4404 kJ
q = 9.7 kJ
W = EC - q = 0.4404 - 9.7 = -9.2596 kJ
  

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