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3 years ago

Calculate the theoretical efficiency for an Otto cycle engine with γ=1.40 and compression ration r=9.50.

Engineering

1 answer:

DENIUS [597]3 years ago

7 0

Answer:

The theoretical efficiency of the Otto engine is 59.4 percent.

Explanation:

The theoretical efficiency for Otto engine ( $\eta$ ), dimensionless, is obtained by this formula after supossing that fluid is an ideal gas:

$\eta = 1-\frac{1}{r^{\gamma -1}}$

Where:

$r$ - Compression ratio, dimensionless.

$\gamma$ - Heat capacity ratio, dimensionless.

Given that $r = 9.50$ and $\gamma = 1.40$ , the theoretical efficiency of the Otto engine is:

$\eta = 1 - \frac{1}{9.50^{1.40-1}}$

$\eta = 0.594$

The theoretical efficiency of the Otto engine is 59.4 percent.

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3 years ago

There are 22 gloves in a drawer: 5 pairs of red gloves, 4 pairs of yellow, and 2 pairs of green. You select the gloves in the da

antiseptic1488 [7]

Answer:

Best case = 2 gloves

Given Information:

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smallest number of gloves you need to select to have at least one matching pair in the best case = ?

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How many gloves do you need to make one matching pair?

Yes, you are right. 2 gloves makes a matching pair and it is the smallest number of gloves you need to select to have at least one matching pair.

But what about worst case?

lets say

you tried all 5 red gloves either all of them were left or right

then you tried 4 yellow gloves either all of them were left or right

then you tried 2 green gloves either all of them were left or right

Now all the left or right gloves are tried (5 + 4 + 2 = 11) and the 12th one will definitely be either matching red, yellow or green.

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3 years ago

Thermal energy storage systems commonly involve a packed bed of solid spheres, through which a hot gas flows if the system is be

zheka24 [161]

Answer:

as the exercise is incomplete, I add the information that is missing:

Consider a packed bed of 75-mm-diameter aluminum spheres ? = 2700 kg/m3, and c = 950 J/kg

Answer: The copper can store 34.1% more thermal energy at 272.42ºC

Explanation:

Given:

Diameter packed bed = 75 mm

Density = 2700 kg/m³

specific heat = 950 J/kg K

initial temperature sphere = 25ºC

thermal conductivity = 240 W/m K

temperature of gas = 300ºC

convection coefficient = 75 W/m²K

The characteristic length is

$L_{c} =\frac{r}{3} =\frac{0.0375}{3} =0.0125m$

The Biot number is equal to

$Bi=\frac{hL_{c} }{k} =\frac{75*0.0125}{240} =3.9x10^{-6}$

Bi < 1, we will use the lumped capacitance method

The energy transfer is equal to:

$\frac{Q}{Q_{max} } =(1-exp(\frac{t}{t_{t} } ))$ (eq. 1)

$t_{t} =\frac{pV}{hA} =\frac{p\frac{\pi D^{3} }{6} c}{h\pi D^{2} } =\frac{pDc}{6h} \\t_{t}=\frac{2700*0.075*950}{6*75} =427.5s$

Replacing in eq. 1

$0.9=1-exp(\frac{-t}{t_{t} } )\\0.1=exp(\frac{-t}{t_{t} } )\\\frac{-t}{t_{t} } =ln(0.1)\\t=2.3t_{t}=2.3*427.5=983.25s$

The temperature at the center of sphere is

$T=T\alpha +(T_{i} -T\alpha )exp(\frac{-6ht}{pDc} )=300+(25-300)exp(\frac{-6*75*983.25}{2700*0.075*950} )=272.42C$

We obtain the percentage increase

Cpcu = 385 J/kg K

(pCp)cu = 8933 * 385 = 3439205 J/m³K

from water:

(pCp)wa = 2700 * 950 = 2565000 J/m³K

the percentage increase is

%P = (3439205 - 2565000)/2565000 = 34.1%

The copper can store 34.1% more thermal energy.

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3 years ago