Question

An astronaut performing an extra-vehicular activity (space walk) shaded from the Sun is wearing a spacesuit that can be approximated as perfectly white (e=0) except for a 5cm×8cm patch in the form of the astronaut’s national flag. The patch has emissivity 0.300. The spacesuit under the patch is 0.500 cm thick, with a thermal conductivity k=0.0600 W/m°C, and its inner surface is at a temperature of 20.0°C. What is the temperature of the patch, and what is the rate of heat loss through it? Assume the patch is so thin that its outer surface is at the same temperature as the outer surface of the spacesuit under it. Also assume the temperature of outer space is 0 K.

a) Calculate the temperature of the patch and the rate of heat loss.
b) The problem is unsolvable without the patch's color.
c) The emissivity of the patch is irrelevant to the solution.
d) Heat loss cannot be determined without knowing the astronaut's activity.

Answer 1

The temperature of the astronaut's patch and the rate of heat loss can be calculated using the given emissivity, thermal conductivity, and temperature data by applying both Fourier's law and the Stefan-Boltzmann law. Relevant principles from thermodynamics and heat transfer are used, and the problem can be solved numerically.

Step-by-step explanation:

Calculating Temperature and Heat Loss of an Astronaut's Patch

The question relates to the calculation of the temperature of the patch on an astronaut's spacesuit and the rate of heat loss through it using the principles of thermodynamics and heat transfer. The key data provided are the patch's emissivity, the spacesuit material's thermal conductivity, and the temperature of the spacesuit's inner surface. By comparing this scenario with other problems that involve the Stefan-Boltzmann law and its applications, we infer that the temperature calculation involves solving a numerically challenging equation, and the heat loss can be determined once the temperature is known.

The emissivity is indeed relevant, as it will affect the rate at which the patch radiates heat energy into space. Since the astronaut's spacesuit is shaded from the Sun, radiation is the primary mode of heat transfer for the patch. The rate of heat loss can be determined using the Stefan-Boltzmann law, taking into account the area of the patch and the temperatures involved.

To solve this problem, one must set up the equation using Fourier's law for conductive heat transfer through the spacesuit material and the Stefan-Boltzmann law for radiative heat loss from the patch. The numerical solution can be done using graphing calculators or software that can handle iterative processes for non-linear equations. Details such as the color of the patch can affect emissivity, if not explicitly mentioned, but for the purposes of this problem, we can work with the given emissivity value. Therefore, option (a) is the correct approach to finding the temperature of the patch and the rate of heat loss through it.