5) You have a monatomic ideal gas where n= 0.122 moles. At point 1 on the figure

Question

5) You have a monatomic ideal gas where n= 0.122 moles. At point 1 on the figure, the temperature is 300 K. Shown are two routes (solid line route and dashed line route).
For this problem, you can use either Joules or L×atm for energy units. Note: 1 L×atm = 101.325 Joules
First the system moves from point 1 to point 3 in two steps (solid line in the figure):
1 to 2: ISOTHERMAL expansion from 1 to 3 L (pressure drops from 3 to 1 atm)
2 to 3: ISOVOLUMETRIC drop in pressure (pressure drops from 1 to 0 4806 atm)

a) Obtain the work done by the system along this route. (solid lines)
b) Obtain the heat added along this route. (solid lines)

c) Now look at the dashed route. In this case the process is adiabatic and quasi-static. Obtain the work done by the system along this route. (dashed line)
d) Obtain the heat added along this route. (dashed line)

please help asap thanks!!

Explanation / Answer

(A)

work done = 2.303*n*R*T*log(v2/v1) = 2.303*0.122*8.314*300*log(3/1)

W1-2 = 334.36 J

w2-3 = 0

w13 = 334.36 J

(b)

u1-2 = 0

u2-3 = (p3-p2)*v/(gamma-1)

U2-3 = (0.4806-1)*3*101.325/( 1.67-1) = -235.65 J

Q = -235.65 + 334.36 = 98.71 J

(c)

W = (P1*v1 - P3*v3)/(gamma-1)

W = (3-(0.4806*3))*101.325/(1.67-1)

W = 235.65 J

(d)

Q = 0

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