- #1

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a) Estimate the rate of rise of the leaf’s temperature. (ans: 2.3 oC/s)

b) Calculate the temperature of leaf would reach if it lost all its heat by radiation (the surroundings are at 20 oC). (ans: 84 oC)

How to do this question??

Any hints?

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- Thread starter frozen7
- Start date

- #1

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a) Estimate the rate of rise of the leaf’s temperature. (ans: 2.3 oC/s)

b) Calculate the temperature of leaf would reach if it lost all its heat by radiation (the surroundings are at 20 oC). (ans: 84 oC)

How to do this question??

Any hints?

- #2

mukundpa

Homework Helper

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What is the rate at which it receives heat? Intensity of sun's radiation at that place is not given.

- #3

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That`s all the information i have. Does it mean more information is needed to solve this question?

- #4

Tom Mattson

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[tex]I=\frac{P}{4\pi r^2}[/tex],

where [itex]r[/itex] is the Sun-Earth distance.

- #5

Integral

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- #6

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I optain the value of another temperature after using this value in radiation formula. However,how to find the rate of rise of temperature?

- #7

mukundpa

Homework Helper

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dU/dt = I A = mc dT/dt

m is the mass and c is specific heat of the material. with proper units you will get dT/dt.

Absorbity is not mentioned hear but I think it is equal to emissivity of the surface.

For the second part you can use stefan's law of radiation, the radiant heat must be equal to heat absorbed.

- #8

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mukundpa said:dU/dt = I A = mc dT/dt

Why dU/dT = IA? But not supposed to be IeA The given e of leaf is 0.85. How come substitute e = 1?

- #9

mukundpa

Homework Helper

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mukundpa said:Absorbity is not mentioned here but I think it is equal to emissivity of the surface.

I think you have missed it.

- #10

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IeA = solar energy

1000(0.85)(20cm^2) = [tex]\sigma[/tex] (T^4) (Surface area of Sun)

T = xxx

Is it?

If so, how to find the rate of rise of temperature then?

- #11

mukundpa

Homework Helper

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IeA = m c dT/dt Where m is the mass, c is specific heat and T is temperature.

- #12

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erm.....why IeA = m c dT/dt ??

- #13

mukundpa

Homework Helper

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Specific heat (c) is the amount of heat required to raise the temperature of unit mass of the substance by 1 degree. To make per unit time we have to divide it by time and hence dT/dt will give the rate of increase in the temperature.

O.K.?

- #14

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OK..Thanks for it.

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