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2 years ago

What is the rate of heat transfer required to melt 1-ton of ice at 32 F in 24 hours?

Mathematics

1 answer:

LiRa [457]2 years ago

8 0

Answer:

3865.74 J/s

Step-by-step explanation:

mass of ice, m = 1 ton = 1000 kg

time , t = 24 hours

latent heat of fusion of ice, L = 334000 J/kg

Heat required to melt, H = m x L

where, m is the mass of ice and L be the latent heat of fusion

So, H = 1000 x 334000 = 334 xx 10^6 J

Rate of heat transfer = heat / time = $\frac{334\times 10^{6}}{86400}$

Rate of heat transfer = 3865.74 J/s

thus, the rate of heat transfer is 3865.74 J/s.

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Given: R=2m

mr_godi [17]

Answer:

$V = \frac{2L\sqrt{3}}{3} \pi}$

$A = 4\pi + \sqrt{3L^{2} + 16}$

Step-by-step explanation:

Figure of cone is missing. See attachment

Given

Radius, R = 2m

Let L = KL=LM=KM

Required:

Volume, V and Surface Area, A

Calculating Volume

Volume is calculated using the following formula

$V = \frac{1}{3} \pi R^{2} H$

Where R is the radius of the cone and H is the height

First, we need to determine the height of the cone

The height is represented by length OL

It is given that KL=LM=KM in triangle KLM

This means that this triangle is an equilateral triangle

where OM = OK = $\frac{1}{2} KL$

OK = $\frac{1}{2}L$

Applying pythagoras theorem in triangle LOM,

|LM|² = |OL|² + |OM|²

By substitution

L² = H² + ( $\frac{1}{2}L$ )²

H² = L² - $\frac{1}{4}L$ ²

H² = L² (1 - $\frac{1}{4}$ )

H² = L² $\frac{3}{4}$

H² = $\frac{3L^{2} }{4}$

Take square root of bot sides

$H = \sqrt{\frac{3L^{2} }{4}}$

$H = \frac{L\sqrt{3}}{2}$

Recall that $V = \frac{1}{3} \pi R^{2} H$

$V = \frac{1}{3} \pi 2^{2} * \frac{L\sqrt{3}}{2}$

$V = \frac{1}{3} \pi * 4} * \frac{L\sqrt{3}}{2}$

$V = \frac{1}{3} \pi} * {2L\sqrt{3}}$

$V = \frac{2L\sqrt{3}}{3} \pi}$

in terms of $\pi$ an d L where L = KL = LM = KM

Calculating Surface Area

Surface Area is calculated using the following formula

$H = \frac{L\sqrt{3}}{4}$

$A=\pi r(r+\sqrt{h^{2} +r^{2} } )$

$A=\pi * 2(2+\sqrt{((\frac{L\sqrt{3}}{2})^{2} +2^{2} } )$ )

$A=\pi * 2(2+\sqrt{{\frac{3L^{2}}{4} } + 4 }$ )

$A=\pi * 2(2+\sqrt{{\frac{3L^{2}+16}{4} } })$

$A=2\pi(2+\sqrt{{\frac{3L^{2}+16}{4} } })$

$A = 2\pi (2 + \frac{\sqrt{3L^{2} + 16}}{\sqrt{4}} )$

$A = 2\pi (2 + \frac{\sqrt{3L^{2} + 16}}{2} )$

$A = 2\pi (2 + {\frac{1}{2} \sqrt{3L^{2} + 16})$

$A = 4\pi + \sqrt{3L^{2} + 16}$

6 0

2 years ago

I have 3 green cubes, 4 red cubes, 2 black cubes, and 6 yellow cubes. What is the probability that I will randomly choose a blac

Strike441 [17]

Answer:

4/75 or 0.05333

Step-by-step explanation:

3+4+2+6=15 elements

2/15= probability to choose a black

6/15 = probability to choose a yellow cube

Probability to choose a black AND (*) a yellow = 2/15*6/15=12/225=4/75 or 0.05333

6 0

2 years ago

Connor is asked to find the probability of rolling a prime number on a die. He states that this is a simple event. True or false

Dafna1 [17]

The correct answer is true

5 0

2 years ago

6. What is the Greatest Common Factor of 45 and 60? 14560

bazaltina [42]

Answer:

15 15 goes into 45 5 times and 60 5 times. highest number that goes into both numbers evenly

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2 years ago

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-2 (t+2) +5 t = 6 t + 11

vovikov84 [41]

Answer:

The answer is T=-5

Step-by-step explanation:

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2 years ago

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