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College Physics (Urone)
Found in: Page 506
College Physics (Urone)

College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

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Short Answer

Radiation makes it impossible to stand close to a hot lava flow. Calculate the rate of heat transfer by radiation from \({\bf{1}}{\bf{.00}}\;{{\bf{m}}^{\bf{2}}}\) of 1200ºC fresh lava into 30.0ºC surroundings, assuming lava’s emissivity is 1.00.

The rate of heat transfer from lava by radiation is \({\bf{2}}{\bf{.664 \times 1}}{{\bf{0}}^{\bf{5}}}\;{\bf{J/s}}\).

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Determination of formula for rate of heat transfer from lava by radiationGiven Data:

The area of fireplace is \(A = 1\;{{\rm{m}}^2}\)

The temperature of fresh lava is \({T_1} = 1200^\circ {\rm{C}} = 1473\;{\rm{K}}\)

The temperature of surrounding is \({T_2} = 30^\circ {\rm{C}} = 303\;{\rm{K}}\)

The emissivity of lava is \(\varepsilon = 1\)

The radiant energy transfer is calculated by using the Stefan’s law. This law gives the energy transfer without any medium.

The rate of heat transfer from lava by radiation is given as:

\(Q = \varepsilon \sigma A\left( {T_1^4 - T_2^4} \right)\)

Here, \(\sigma \) is Stefan’s constant and its value is \(5.67 \times {10^{ - 8}}\;{\rm{W}} \cdot {{\rm{m}}^{ - 2}} \cdot {{\rm{K}}^4}\)

Step 2: Determination of rate of heat transfer from lava by radiation

Substitute all the values in the above equation.

\(\begin{aligned}{}Q &= \left( 1 \right)\left( {5.67 \times {{10}^{ - 8}}\;{\rm{W}} \cdot {{\rm{m}}^{ - 2}} \cdot {{\rm{K}}^4}} \right)\left( {1\;{{\rm{m}}^2}} \right)\left( {{{\left( {1473\;{\rm{K}}} \right)}^4} - {{\left( {303\;{\rm{K}}} \right)}^4}} \right)\\Q &= 2.664 \times {10^5}\;{\rm{W}}\\Q &= \left( {2.664 \times {{10}^5}\;{\rm{W}}} \right)\left( {\frac{{1\;{\rm{J}}/{\rm{s}}}}{{1\;{\rm{W}}}}} \right)\\Q &= 2.664 \times {10^5}\;{\rm{J}}/{\rm{s}}\end{aligned}\)

Therefore, the rate of heat transfer from lava by radiation is \(2.664 \times {10^5}\;{\rm{J}}/{\rm{s}}\).

Most popular questions for Physics Textbooks

When heat transfers into a system, is the energy stored as heat? Explain briefly.

Suppose you walk into a sauna that has an ambient temperature of 50.0ºC . (a) Calculate the rate of heat transfer to you by radiation given your skin temperature is 37.0ºC , the emissivity of skin is 0.98, and the surface area of your body is \({\bf{1}}{\bf{.50}}\;{{\bf{m}}^{\bf{2}}}\). (b) If all other forms of heat transfer are balanced (the net heat transfer is zero), at what rate will your body temperature increase if your mass is 75.0 kg?

(a) How much heat transfer is necessary to raise the temperature of a \({\rm{0}}{\rm{.200 kg}}\) piece of ice from\({\rm{ - 2}}{{\rm{0}}^{\rm{o}}}{\rm{C}}\)to \({\rm{ - 130}}{{\rm{}}^{\rm{o}}}{\rm{C}}\) , including the energy needed for phase changes?

(b) How much time is required for each stage, assuming a constant\({\rm{20}}{\rm{.0 kJ/s}}\)rate of heat transfer?

(c) Make a graph of temperature versus time for this process.

In very humid climates where there are numerous bodies of water, such as in Florida, it is unusual for temperatures to rise above about 35o .C (95o)F In deserts, however, temperatures can rise far above this. Explain how the evaporation of water helps limit high temperatures in humid climates.

(a) Cherry-red embers in a fireplace are at 850ºC and have an exposed area of \({\bf{0}}{\bf{.200}}\;{{\bf{m}}^{\bf{2}}}\) and an emissivity of 0.980. The surrounding room has a temperature of 18.0ºC. If 50% of the radiant energy enters the room, what is the net rate of radiant heat transfer in kilowatts? (b) Does your answer support the contention that most of the heat transfer into a room by a fireplace comes from infrared radiation?
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