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Figure p2. 54 shows a gas contained in a vertical piston–cylinder assembly. A vertical shaft whose cross-sectional area is 0. 8 cm2 is attached to the top of the piston. The total mass of the piston and shaft is 25 kg. While the gas is slowly heated, the internal energy of the gas increases by 0. 1 kj, the potential energy of the piston–shaft combination increases by 0. 2 kj, and a force of 1334 n is exerted on the shaft as shown in the figure. The piston and cylinder are poor conductors, and friction between them is negligible. The local atmospheric pressure is 1 bar and g = 9. 81 m/s2. Determine, (a) the work done by the shaft, (b) the work done in displacing the atmosphere, and (c) the heat transfer to the gas, all in kj. (d) using calculated and given data, develop a detailed accounting of the heat transfer of energy to the gas.

Sagot :

A)  The work done by the shaft is; W_s = 1.08721 kJ

B) The work done in displacing the atmosphere is; W_atm = 1.4337 kJ

C) The heat transfer to the gas is; Q = 2.821 kJ

D) The detailed account of the heat transfer of energy to the gas is; done using concept of first law of thermodynamics

Understanding First Law of Thermodynamics

From the attached image, we see the vertical piston-cylinder assembly and we are given the values;

Mass of piston and shaft; m = 25 kg

Change in potential energy; ΔPE = 0.2 kJ = 200 J

Force Exerted; F_s = 1334 N

Diameter of Piston; D = 15 cm

Area of Shaft; A_shaft = 0.8 cm²

Atmospheric Pressure; P_atm = 1 bar = 100000 Pa

Change in internal energy of gas; ΔU_gas = 0.1 kJ = 100 J

A) Let us first find the change in height from;

ΔPE = mg*Δz

Δz = ΔPE/(mg)

Δz = 200/(25 * 9.81)

Δz = 0.815 m

Work done by shaft is gotten from the formula;

W_s = F_s * Δz

W_s = 1334 * 0.815

W_s = 1087.21 J

W_s = 1.08721 kJ

B) The net area is gotten from;

A_net = A_piston - A_shaft

A_net = ((π * 15²)/4) - 0.8

A_net = 175.915 cm² = 0.0175915 m²

Work done against the atmosphere is;

W_atm = P_atm * A_net * Δz

W_atm = 100000 * 0.0175915 * 0.815

W_atm = 1433.7 J

W_atm = 1.4337 kJ

C) Total work done by the system is gotten from;

W = W_s + W_atm

W = 1087.21 + 1433.7

W = 2,520.91 J

W = 2.521 kJ

From first law of thermodynamics we can arrive at;

Q = ΔU_gas + ΔPE_piston and shaft + W

Plugging in the relevant values gives;

Q = 100 + 200 + 2,520.91

Q = 2820.91 J

Q = 2.821 kJ

Read more about first law of thermodynamics at; https://brainly.com/question/15071682

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