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.

Q2:

The intensity of the radiation of sunlight at a distance from the Sun of 1 0 8 × 1 0 6 km is measured to be 2 6 0 0 W/m2.

Calculate the radiative power of the Sun.

  • A 3 . 8 × 1 0 2 5 W
  • B 7 . 6 × 1 0 2 6 W
  • C 7 . 6 × 1 0 2 5 W
  • D 3 . 8 × 1 0 2 6 W
  • E 1 . 9 × 1 0 2 6 W

Calculate the radius of the Sun. Use a value of 6 . 0 × 1 0 3 K for the Sun’s temperature and use a value of 1.0 for the Sun’s emissivity.

  • A 6 . 4 × 1 0 6 km
  • B 6 . 6 × 1 0 6 km
  • C 6 . 2 × 1 0 6 km
  • D 3 . 2 × 1 0 6 km
  • E 0 . 3 × 1 0 6 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 4 0 0 km for the radius of Mars.

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

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 1 5 0 C . 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?

  • AConvection, isobaric, and radiation.
  • BRadiation, friction, and convection.
  • CConduction, isothermal, and isentropic.
  • DConduction, convection, and radiation.

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