A sphere of surface area 1.25 m² and emissivity 1.0 is at a temperature of 100°C. At what rate does it radiate heat into empty space? (o= 5.67 x 10-8 W/m2. K4) O 3.7 W O 0.71 mW O 1.4 kW O 7.1 W O 9.9 mW
Energy transfer
The flow of energy from one region to another region is referred to as energy transfer. Since energy is quantitative; it must be transferred to a body or a material to work or to heat the system.
Molar Specific Heat
Heat capacity is the amount of heat energy absorbed or released by a chemical substance per the change in temperature of that substance. The change in heat is also called enthalpy. The SI unit of heat capacity is Joules per Kelvin, which is (J K-1)
Thermal Properties of Matter
Thermal energy is described as one of the form of heat energy which flows from one body of higher temperature to the other with the lower temperature when these two bodies are placed in contact to each other. Heat is described as the form of energy which is transferred between the two systems or in between the systems and their surrounding by the virtue of difference in temperature. Calorimetry is that branch of science which helps in measuring the changes which are taking place in the heat energy of a given body.
![### Radiative Heat Transfer Problem
#### Problem Statement:
A sphere of surface area \(1.25 \, \text{m}^2\) and emissivity \(1.0\) is at a temperature of \(100^\circ\text{C}\). At what rate does it radiate heat into empty space? \(( \sigma = 5.67 \times 10^{-8} \, \text{W/m}^2 \cdot \text{K}^4)\)
#### Multiple Choice Answers:
- \( \boxed{3.7 \, \text{W}} \)
- \( \boxed{0.71 \, \text{mW}} \)
- \( \boxed{1.4 \, \text{kW}} \)
- \( \boxed{7.1 \, \text{W}} \)
- \( \boxed{9.9 \, \text{mW}} \)
#### Explanation:
To solve this problem, we can use the Stefan-Boltzmann law which states:
\[ P = \sigma \cdot A \cdot e \cdot T^4 \]
Where:
- \(P\) is the power radiated (in Watts, W),
- \( \sigma \) is the Stefan-Boltzmann constant \(( 5.67 \times 10^{-8} \, \text{W/m}^2 \cdot \text{K}^4)\),
- \(A\) is the surface area \(( 1.25 \, \text{m}^2)\),
- \(e\) is the emissivity, which is 1.0 in this case (since it is a perfect black body),
- \(T\) is the temperature in Kelvin (need to convert from Celsius to Kelvin by adding 273.15).
Substitute the given values:
1. Convert the temperature to Kelvin:
\[ 100^\circ\text{C} = 100 + 273.15 = 373.15 \, \text{K}\]
2. Apply the Stefan-Boltzmann law:
\[ P = 5.67 \times 10^{-8} \, \text{W/m}^2 \cdot \text{K}^4 \times 1.25 \, \text{m}^2 \times 1.0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec99e2ce-f146-4dfd-8358-2828b726596b%2F9142879a-905d-4698-b954-47a864c28239%2Fbqkzq9m_processed.jpeg&w=3840&q=75)
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