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2 years ago

Helium gas expands in a piston-cylinder in a polytropic process with n=1.67. Is the work positive, negative or zero?

Engineering

1 answer:

IRINA_888 [86]2 years ago

3 0

Answer:

work will be positive when it is under polytropic expansion process

Explanation:

It states a polytropic process with n equal to 1.67. there is a polytropic expansion that mean work is positive and if it was polytropic compression then it would be negative

$PV^n = const$

$P_1V_1 = P_2V_2$

Also work during the process of polytropic is given as

$W_{1-2} =\frac{P_1V_1 -P_2V_2}{n-1}$

the work will be positive when it is under the polytropic expansion process

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1 year ago

A gasoline engine has a piston/cylinder with 0.1 kg air at 4 MPa, 1527◦C after combustion, and this is expanded in a polytropic

Roman55 [17]

Answer:

The expansion work is 71.24 kJ and heat transfer is -16.89 kJ

Explanation:

From ideal gas law,

Initial volume (V1) = nRT/P

n is the number of moles of air in the cylinder = mass/MW = 0.1/29 = 0.00345 kgmol

R is gas constant = 8314.34 J/kgmol.K

T is initial temperature = 1527 °C = 1527+273 = 1800 K

P is initial pressure = 4 MPa = 4×10^6 Pa

V1 = 0.00345×8314.34×1800/(4×10^6) = 0.013 m^3

V2 = 10×V1 = 10×0.013 = 0.13 m^3

The process is a polytropic expansion process

polytropic exponent (n) = 1.5

P2 = P1(V1/V2)^n = 4×10^6(0.013/0.13)^1.5 = 1.26×10^5 Pa

Expansion work = (P1V1 - P2V2) ÷ (n - 1) = (4×10^6 × 0.013 - 1.26×10^5 × 0.13) ÷ (1.5 - 1) = 35620 ÷ 0.5 = 71240 J = 71240/1000 = 71.24 kJ

Heat transfer = change in internal energy + expansion work

change in internal energy (∆U) = Cv(T2 - T1)

T2 = PV/nR = 1.26×10^5 × 0.13/0.00345×8314.34 = 571 K

Cv = 20.785 kJ/kgmol.K

∆U = 20.785(571 - 1800) = -25544.765 kJ/kgmol × 0.00345 kgmol = -88.13 kJ

Heat transfer = -88.13 + 71.24 = -16.89 kJ

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2 years ago

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An engineer lives in Hawaii at a location where the annual rain fall is 300 inches. She decides to use the rain to generate elec

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Answer:

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Explanation:

Flow rate of water in the system = 3.6x10^-6

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Q = 3.6x10^-6/[1/3600]

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2 years ago