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murzikaleks [220]
3 years ago
9

A gas within a piston–cylinder assembly undergoes an isothermal process at 400 K during which the change in entropy is 20.3 kJ/K

. Assuming the ideal gas model for the gas and negligible kinetic and potential energy effects, evaluate the work, in kJ.
Engineering
1 answer:
Mashcka [7]3 years ago
8 0

Answer:

W= 8120 KJ

Explanation:

Given that

Process is isothermal ,it means that temperature of the gas will remain constant.

T₁=T₂ = 400 K

The change in the entropy given ΔS = 20.3 KJ/K

Lets take heat transfer is Q ,then entropy change can be written as

\Delta S=\dfrac{Q}{T}

Now by putting the values

20.3=\dfrac{Q}{400}

Q= 20.3 x 400 KJ

Q= 8120 KJ

The heat transfer ,Q= 8120 KJ

From first law of thermodynamics

Q = ΔU + W

ΔU =Change in the internal energy ,W=Work

Q=Heat transfer

For ideal gas ΔU  = m Cv ΔT]

At constant temperature process ,ΔT= 0

That is why ΔU  = 0

Q = ΔU + W

Q = 0+ W

Q=W= 8120 KJ

Work ,W= 8120 KJ

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Answer:

The fin temperature in °C at a distance of 10 cm from the base = 33.78°C

Explanation:

The following assumptions will be made to solve this problem

- The heat transfer coefficient does not change with the time or distance.

- The temperature of the fins varies just in only one direction.

The temperature of the fin at x = 10 cm = 0.10 m from the base can be calculated from the temperature variation with distance formula for a very long fin.

(T - T∞) = (T₀ - T∞)e⁻ᵐˣ

T = T(x) = temperature at any point along the fin

T∞ = temperature at the tip of the fin = ambient temperature = 25°C

T₀ = temperature at the base of thw fin = 50°C

x = any distance along the length of the fin from the base of the fin = 0.1 m

m = √(hP/KA)

h = Heat transfer coefficient = 123 W/m².K

P = perimeter in contact with the base = πD = π × 0.03 = 0.0943 m

K = thermal conductivity = 150 W/m.K

A = surface area in contact with the base = πD²/4 = π(0.03)²/4 = 0.0007071 m²

m = √(123 × 0.0943)/(150 × 0.0007071)

m = 10.46

mx = 10.46 × 0.1 = 1.046

(T - 25) = (50 - 25) e⁻¹•⁰⁴⁶

T = 25 + 25 e⁻¹•⁰⁴⁶ = 25 + 8.78 = 33.78°C

8 0
2 years ago
The human circulatory system consists of a complex branching pipe network ranging in diameter from
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Answer: the average velocity decreases

Explanation:

From the provided data we have:

Vessel    avg. diameter[mm] number

Aorta                 25.0                   1

Arteries             4.0                    159

Arteioles           0.06                 1.4*10^7

Capillaries         0.012               2.9*10^9

from the information, let \hat{m} be the mass flow rate, \rho is density, n number of vessels, and A is the cross-section area for each vessel

the flow rate is constant so it is equal for all vessels,

The average velocity is related to the flow rate by:

\hat{m} = v* \rho * A * n

we clear the side where v is in:

v = \frac{\hat{m}}{\rho A n}

area is π*R^2 where R is the average radius of the vessel (diameter/2)

we get:

v = \frac{\hat{m}}{\rho \pi R^2 n}

you can directly see in the last equation that if we go from the aorta to the capillaries, the number of vessels is going to increase ( n will increase and R is going to decrease ) . From the table, R is significantly smaller in magnitude orders than n, therefore, it wont impact the results as much as n. On the other hand, n will change from 1 to 2.9 giga vessels which will dramatically reduce the average blood velocity

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3 years ago
The denominator of a fraction is 4 more than the numenator. If 4 is added to the numenator and 7 is added to the denominator, th
kati45 [8]

Answer:

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Explanation:

Lets take the numerator of the fraction to be = x

So the denominator of the fraction is 4 more than the numerator = x+4

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Now add 4 to the numerator and add 7 to the denominator as;

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This new fraction is equal to 1 half =1/2

write the equation as;

\frac{x+4}{x+11} =\frac{1}{2}

perform cross-product

2(x+4 )=1( x+11 )

2x+8 = x + 11

2x-x = 11-8

x=3

The original fraction is;  

\frac{x}{4+x} =\frac{3}{3+4} =\frac{3}{7}

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