A body at a temperature of 727^∘ C and has surface area 5 cm^2, radiates 300 J of energy each

step 1 In this question, it is given that the body has a temperature of 727 degrees centigrade and has

A body at a temperature of 727^∘ C and has surface area 5...

A body at a temperature of $727^{\circ} \mathrm{C}$ and has surface area $5 \mathrm{~cm}^{2}$, radiates $300 \mathrm{~J}$ of energy each minute. The emissivity is : (Given: Boltzmann constant $=5.67 \times 10^{-8}$ watt $\mathrm{m}^{2}(\mathrm{~K})^{4}$ ) (a) $e=0.18$ (b) $e=0.02$ (c) $e=0.2$ (d) $e=0.15$

A body at a temperature of $727^{\circ} \mathrm{C}$ and has surface area $5 \mathrm{~cm}^{2}$, radiates $300 \mathrm{~J}$ of energy each minute. The emissivity is :
(Given: Boltzmann constant $=5.67 \times 10^{-8}$ watt $\mathrm{m}^{2}(\mathrm{~K})^{4}$ )
(a) $e=0.18$
(b) $e=0.02$
(c) $e=0.2$
(d) $e=0.15$

Key Concepts

Unit Conversion

Proper conversion of units (for example, converting surface area from square centimeters to square meters and time or energy to consistent SI units) is crucial for correctly applying physical laws in thermodynamics and heat transfer. This ensures that the calculated values are appropriate and consistent with the constants used in the equations.

Stefan-Boltzmann Law

This physical law relates the power radiated by a body to its temperature and surface area. It states that the radiant energy emitted per unit area is proportional to the fourth power of the absolute temperature, scaled by the Stefan-Boltzmann constant. This law is fundamental in thermal radiation and is used for calculating energy loss from bodies by radiation.

Emissivity

Emissivity is a dimensionless factor between 0 and 1 that indicates how effectively a real surface emits thermal radiation compared to an ideal black body. It accounts for the material’s surface properties and plays a critical role in the Stefan-Boltzmann law when determining the actual radiant energy emitted by the surface.

Temperature Unit Conversion

In thermal calculations, temperature must be expressed in absolute scale (Kelvin) rather than Celsius or Fahrenheit. Converting temperatures properly is essential for accurate application of laws such as the Stefan-Boltzmann law since it relies on the absolute temperature raised to the fourth power.

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