Worksheet: Thermal Radiation

In this worksheet, we will practice using the Stefan–Boltzmann law to calculate the intensity of thermal radiation emitted by an object of a given temperature.

Q1:

An infrared heater for a sauna has a surface area of 0.050 m2 and an emissivity of 0.84. What temperature must it run at if the required power is 360 W? Neglect the temperature of the environment. Where Stefan-Boltzman constant = 5.67×10/JsmK.

Q2:

The intensity of the radiation of sunlight at a distance from the Sun of 108×10 km is measured to be 2600 W/m2.

Calculate the radiative power of the Sun.

  • A 1 . 9 × 1 0 W
  • B 7 . 6 × 1 0 W
  • C 7 . 6 × 1 0 W
  • D 3 . 8 × 1 0 W
  • E 3 . 8 × 1 0 W

Calculate the radius of the Sun. Use a value of 6.0×10 K for the Sun’s temperature and use a value of 1.0 for the Sun’s emissivity.

  • A 6 . 2 × 1 0 km
  • B 6 . 6 × 1 0 km
  • C 0 . 3 × 1 0 km
  • D 3 . 2 × 1 0 km
  • E 6 . 4 × 1 0 km

Q3:

Thermal radiation from the Sun has an intensity 𝑆 of about 600 W/m2 at the radius of Mars’s orbit. Assume the Sun is a perfect sphere and its temperature is uniform. Ignore any greenhouse effects.

Assuming the Sun’s rays are parallel, Find the area that 𝑆 must be multiplied by to get the total radiation intercepted by Mars. Use a value of 3,400 km for the radius of Mars.

  • A 7 . 2 6 × 1 0
  • B 1 4 . 5 × 1 0
  • C 1 . 8 2 × 1 0
  • D 3 . 6 3 × 1 0
  • E 2 1 . 4 × 1 0

Find the temperature at which Mars radiates energy at the same rate. Assume that at the infrared wavelengths where it radiates, the emissivity e is 1.00.

Q4:

Heat loss due to radiation for a pipe is 80.0 kW. The pipe is 100.0 m long and its outer radius is 10.0 cm. The surface emissivity of the pipe is 0.70. Find the temperature of the pipe.

Q5:

Calculate heat loss per meter length due to radiation of a metal pipe with an emissivity of 0.930. The temperature of the outer surface of the pipe is 311 K. The outer diameter of the pipe is 15.24 cm.

Q6:

A 100-meter-long pipe is at a temperature of 150C. Find the heat loss due from the pipe due to radiation if the pipe’s outer diameter is 10 cm. The surface emissivity of the pipe is 0.7.

Q7:

What are three major modes of heat transfer?

  • AConduction, isothermal, and isentropic.
  • BRadiation, friction, and convection.
  • CConduction, convection, and radiation.
  • DConvection, isobaric, and radiation.

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