Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 138

Consider a person standing in a room maintained at \(20^{\circ} \mathrm{C}\) at all times. The inner surfaces of the walls, floors, and ceiling of the house are observed to be at an average temperature of \(12^{\circ} \mathrm{C}\) in winter and \(23^{\circ} \mathrm{C}\) in summer. Determine the rates of radiation heat transfer between this person and the surrounding surfaces in both summer and winter if the exposed surface area, emissivity, and the average outer surface temperature of the person are \(1.6 \mathrm{~m}^{2}, 0.95\), and \(32^{\circ} \mathrm{C}\), respectively.

Short Answer

Expert verified
Answer: The rate of radiation heat transfer between the person and the surrounding surfaces in Winter is 170.1 W, and in Summer is 55.6 W.

Step by step solution

01

Convert temperatures to Kelvin

First, we need to convert the given temperatures from Celsius to Kelvin. To do this, add 273.15 to each temperature: 1. Room temperature: \(20 + 273.15 = 293.15\mathrm{~K}\) 2. Inner surfaces temperature (Winter): \(12 + 273.15 = 285.15\mathrm{~K}\) 3. Inner surfaces temperature (Summer): \(23 + 273.15 = 296.15\mathrm{~K}\) 4. Average outer surface temperature of the person: \(32 + 273.15 = 305.15\mathrm{~K}\)
02

Use the Stefan-Boltzmann law

The Stefan-Boltzmann law for radiation heat transfer is given by: $$q = \epsilon\sigma A (T_{1}^{4} - T_{2}^{4})$$ Where \(q\) - rate of radiation heat transfer \(\epsilon\) - emissivity \(\sigma\) - Stefan-Boltzmann constant (\(5.67 \times 10^{-8} \mathrm{W/m^2K^4}\)) \(A\) - exposed surface area \(T_{1}, T_{2}\) - temperatures of the surfaces For our problem, \(\epsilon = 0.95\), \(A = 1.6\mathrm{~m}^2\), \(T_{1} = 305.15\mathrm{~K}\) (person's outer surface temperature) and \(T_{2}\) is the inner surfaces temperature of the house (which varies depending on the season).
03

Calculate radiation heat transfer for Winter season

Substitute the known values for the Winter season into the Stefan-Boltzmann law: $$q_{winter} = 0.95 \times 5.67 \times 10^{-8} \times 1.6 \times (305.15^{4} - 285.15^{4})$$ $$q_{winter} = 170.1\mathrm{~W}$$ The rate of radiation heat transfer between the person and the surrounding surfaces in Winter is \(170.1\mathrm{~W}\).
04

Calculate radiation heat transfer for Summer season

Substitute the known values for the Summer season into the Stefan-Boltzmann law: $$q_{summer} = 0.95 \times 5.67 \times 10^{-8} \times 1.6 \times (305.15^{4} - 296.15^{4})$$ $$q_{summer} = 55.6\mathrm{~W}$$ The rate of radiation heat transfer between the person and the surrounding surfaces in Summer is \(55.6\mathrm{~W}\). In conclusion, the rate of radiation heat transfer between the person and the surrounding surfaces in Winter and Summer are \(170.1\mathrm{~W}\) and \(55.6\mathrm{~W}\), respectively.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The inner and outer surfaces of a \(0.5-\mathrm{cm}\) thick \(2-\mathrm{m} \times 2-\mathrm{m}\) window glass in winter are \(10^{\circ} \mathrm{C}\) and \(3^{\circ} \mathrm{C}\), respectively. If the thermal conductivity of the glass is \(0.78 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), determine the amount of heat loss through the glass over a period of \(5 \mathrm{~h}\). What would your answer be if the glass were \(1 \mathrm{~cm}\) thick?

On a still clear night, the sky appears to be a blackbody with an equivalent temperature of \(250 \mathrm{~K}\). What is the air temperature when a strawberry field cools to \(0^{\circ} \mathrm{C}\) and freezes if the heat transfer coefficient between the plants and air is \(6 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) because of a light breeze and the plants have an emissivity of \(0.9\) ? (a) \(14^{\circ} \mathrm{C}\) (b) \(7^{\circ} \mathrm{C}\) (c) \(3^{\circ} \mathrm{C}\) (d) \(0^{\circ} \mathrm{C}\) (e) \(-3^{\circ} \mathrm{C}\)

An electronic package with a surface area of \(1 \mathrm{~m}^{2}\) placed in an orbiting space station is exposed to space. The electronics in this package dissipate all \(1 \mathrm{~kW}\) of its power to the space through its exposed surface. The exposed surface has an emissivity of \(1.0\) and an absorptivity of \(0.25\). Determine the steady state exposed surface temperature of the electronic package \((a)\) if the surface is exposed to a solar flux of \(750 \mathrm{~W} /\) \(\mathrm{m}^{2}\), and \((b)\) if the surface is not exposed to the sun.

A concrete wall with a surface area of \(20 \mathrm{~m}^{2}\) and a thickness of \(0.30 \mathrm{~m}\) separates conditioned room air from ambient air. The temperature of the inner surface of the wall \(\left(T_{1}\right)\) is maintained at \(25^{\circ} \mathrm{C}\). (a) Determine the heat loss \(\dot{Q}(\mathrm{~W})\) through the concrete wall for three thermal conductivity values of \((0.75,1\), and \(1.25 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) and outer wall surface temperatures of \(T_{2}=-15,-10,-5,0,5,10,15,20,25,30\), and \(38^{\circ} \mathrm{C}\) (a total of 11 data points for each thermal conductivity value). Tabulate the results for all three cases in one table. Also provide a computer generated graph [Heat loss, \(\dot{Q}(\mathrm{~W})\) vs. Outside wall temperature, \(\left.T_{2}\left({ }^{\circ} \mathrm{C}\right)\right]\) for the display of your results. The results for all three cases should be plotted on the same graph. (b) Discuss your results for the three cases.

A cylindrical resistor element on a circuit board dissipates \(1.2 \mathrm{~W}\) of power. The resistor is \(2 \mathrm{~cm}\) long, and has a diameter of \(0.4 \mathrm{~cm}\). Assuming heat to be transferred uniformly from all surfaces, determine \((a)\) the amount of heat this resistor dissipates during a 24-hour period, \((b)\) the heat flux, and \((c)\) the fraction of heat dissipated from the top and bottom surfaces.
See all solutions

Recommended explanations on Physics Textbooks

Quantum Physics

Read Explanation

Waves Physics

Read Explanation

Torque and Rotational Motion

Read Explanation

Nuclear Physics

Read Explanation

Work Energy and Power

Read Explanation

Physical Quantities And Units

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free