Energy emitted by radiation from a pipe

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SUMMARY

The heat emission rate from a vertical steam pipe with a diameter of 8 cm and an emissivity of 0.8 at a surface temperature of 950°C is calculated using Stefan's law. The correct heat emission rate, H, for one meter length of the pipe is determined to be approximately 128 Watts or 30.6 Calories/sec/m. However, discrepancies arise when converting temperatures from Celsius to Kelvin, leading to a book answer of 29 Calories/sec/m. The accurate conversion of 950°C to Kelvin is essential for precise calculations.

PREREQUISITES
  • Understanding of Stefan-Boltzmann law and its application in thermal radiation
  • Knowledge of temperature conversion between Celsius and Kelvin
  • Familiarity with the concept of emissivity in thermal physics
  • Basic proficiency in unit conversions, particularly between Watts and Calories
NEXT STEPS
  • Study the application of Stefan's law in different thermal systems
  • Learn about emissivity and its impact on heat transfer in engineering
  • Explore advanced thermal radiation calculations using software tools
  • Investigate the effects of temperature gradients on heat emission rates
USEFUL FOR

Students studying thermodynamics, engineers working on heat transfer systems, and professionals involved in thermal management of industrial processes will benefit from this discussion.

Karol
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Homework Statement


A vertical steam pipe of diameter 8 cm and emissivity e=0.8 has it's surface at 950C. The surrounding air and the temperature of the room and things in it are at 270C.
What is the heat emission rate H from the pipe, for meter length, by radiation?

Homework Equations


Stefan's law: R=e\sigma T^4
\sigma=5.672\times 10^{-8}\left[Watt/m^2\right]
1\left[Calorie\right]=4.186\left[Joule\right]

The Attempt at a Solution


R=0.8\cdot 5.672\times10^{-8}\left(373^4-300^4\right)=511\left[Watt/m^2\right]
H=511\cdot \pi \cdot 0.08\cdot 1=128\left[Watt/m\right]
128\left[Watt\right]\div 4.186=30.6\left[Calorie/Sec/m\right]
The answer, according to the book, is 29\left[Calorie/Sec/m\right]
 
Physics news on Phys.org
95C is ~368K not 373K, though using 368K I get only 28 cal/s/m
 
The book uses Kelvin as Celsius+273
 

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