A gas undergoes an isothermal expansion from V_1 = 1.4L following by isobaric p

Question

A gas undergoes an isothermal expansion from V_1 = 1.4L following by isobaric p = cst compression, if p_1 = 4.4 atm, p_2 = 1.7atm rightarrow ? N/m^2, calculate the work done by gas during the expansion. The total work done by the gas is the sum of the works done for the two processes, isothermal and isobaric. For isothermal processes, Delta T = 0 rightarrow T = cst rightarrow A gas undergoes an isothermal expansion from V_1 = 1.7L following by isobaric p = cst compression, if p_1 = 3.2 atm, p_2 = 1.4atm rightarrow ? N/m^2, calculate the work done by gas during the expansion. The total work done by the gas is the sum of the works done for the two processes, isothermal and isobaric. For isothermal processes, Delta T = 0 rightarrow T = cst rightarrow

Explanation / Answer

V1 = 1.4 x 10^-3 m^3

P1 = 4.4 x 101325 Pa

P! V1 = P2 V2

(4.4) (1.4) = (1.7) (V2) => V2 = 3.62 L = 3.62 x 10^-3 m^3

Work done = P1 V1 ln(V2 / V1)

W1 = (1.4 x 10^-3 x 4.4 x 101325) ln(3.62 / 1.4) = 593.8 J

now P2 = P3 = 1.7 atm

W2= P deltaV = (1.7 x 101325 Pa) (1.4 - 3.62) x 10^-3

= - 382.4 J

total work done = W1 + W2 = 211.4 J .....Ans

-------------------------------------

V1 = 1.7 x 10^-3 m^3

P1 = 3.2 x 101325 Pa

P! V1 = P2 V2

(3.2) (1.7) = (1.4) (V2) => V2 = 3.89 L = 3.89 x 10^-3 m^3

Work done = P1 V1 ln(V2 / V1)

W1 = (1.7 x 10^-3 x 3.2 x 101325) ln(3.89 / 1.7) = 455.7 J

now P2 = P3 = 1.4 tm

W2= P deltaV = (1.4 x 101325 Pa) (1.7 - 3.89) x 10^-3

= - 310.7 J

total work done = W1 + W2 = 145 J .....Ans

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