A gas expands from I to F in the figure below. The energy added to the gas by he

Question

A gas expands from I to F in the figure below. The energy added to the gas by heat is 382 J when the gas goes from I to F along the diagonal path. What is the change in internal energy of the gas? How much energy must be added to the gas by heat along the indirect path IAF? Gas in a container is at a pressure of 5.20 atm and a volume of 1.20 m^3. What is the work done on the gas if it expands at constant pressure to twice its initial volume? Use the expression relating the pressure and change in volume to the work done. J What is the work done on the gas if it is compressed at constant pressure to one-quarter of its initial volume?

Explanation / Answer

(a)

work done in diagonal process = area under the diagonal graph

work = area of rectangle + area of triangle

W = (1.013*10^5*(4-2)*10^-3) + (0.5*2*10^-3*3*1.013*10^5)

W = 506.5 J

U = Q - w = 382 - 506.5 = -124.5 J

(b)

Work done = area under indirect path

W = 4*1.013*10^5*2*10^-3 = 810.4 J

+++++++++++++++++++++++

at constant pressure

work = P*(dV) = P*(V2-v1)

W = P*10^5*(2v1-v1)

W = 5*1.013*10^5*1.2

W = 607800 J

___

(b)

at constant pressure

work = P*(dV) = P*(V2-v1)

v2 = v1/4

W = P1*(v1/4 - v1) = -P1*3v1/4

W = -5.2*1.013*10^5*3*1.2/4

W = -474084 J

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