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erma4kov [3.2K]
4 years ago
15

Water is being heated in a vertical piston-cylinder device. the piston has a mass of 20 kg and a cross-sectional area of 100 cm2

. if the local atmospheric pressure is 100 kpa, determine the temperature at which the water starts boiling.
Physics
1 answer:
sesenic [268]4 years ago
4 0
<span>Answer: We have pressure from the weight of the piston + atmospheric pressure acting on the gas pressure from the piston... P = F / area = mass x acceleration due to gravity / area P = (24 kg x 9.80 m/s²) / (90 cm² x (1m/100cm)²) = 26133 N/m² = 2.61x10^4 Pa = 26.1 kPa total pressure acting on the gas = 26+85 kPa = 111 kPa then.. via clausius clapeyron equation.. ln(P1 / P2) = (dHvap / R) x (1 / T2 - 1 / T1) and if I pick say.. the normal boiling point of water for P2, T2.. then... P1 = 111 kPa P2 = 101.325 kPa dHvap = 40680 J/mole R = 8.314 J/moleK T2 = 373.15 K T1 = ?? ---> T1 = 102.46°</span>
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Consider the differential equation
Zielflug [23.3K]
Yp(t) = A1 t^2 + A0 t + B0 t e(4t)

=> y ' = 2A1t + A0 + B0 [e^(4t) +4 te^(4t) ]

     y ' = 2A1t + A0 + B0e^(4t) + 4B0 te^(4t)

=> y '' = 2A1 + 4B0e(4t) + 4B0 [ e^(4t) + 4te^(4t)

     y '' = 2A1 + 4B0e^(4t) + 4B0e^(4t) + 16B0te^(4t)

Now substitute the values of y ' and y '' in the differential equation:

 
<span>y′′+αy′+βy=t+e^(4t)


</span> 2A1 + 4B0e^(4t) + 4B0e^(4t) + 16B0te^(4t) + α{2A1t + A0 + B0e^(4t) + 4B0 te^(4t) } + β{A1 t^2 + A0 t + B0 t e(4t)} = t + e^(4t)

Next, we equate coefficients

1) Constant terms of the left side = constant terms of the right side:

2A1+ 2αA0 = 0 ..... eq (1)

2) Coefficients of e^(4t) on both sides

8B0 + αB0 = 1 => B0 (8 + α) = 1 .... eq (2)

3) Coefficients on t

2αA1 + βA0 = 1 .... eq (3)


4) Coefficients on t^2

βA1 = 0 ....eq (4)

given that A1 ≠ 0 => β =0

5) terms on te^(4t)

16B0 + 4αB0 + βB0 = 0 => B0 (16 + 4α + β) = 0 ... eq (5)

Given that B0 ≠ 0 => 16 + 4α + β = 0

Use the value of β = 0 found previously

16 + 4α = 0 => α = - 16 / 4 = - 4.

Answer: α = - 4 and β = 0
  




3 0
4 years ago
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