Heat Transfer - Engineering

Q1:

The thermal radiation emitted by a body is proportional to Tn, where T is its absolute temperature. The value of 'n' is exactly 4 for

A black painted bodies only

B all bodies

C polished bodies only

D a black body

ANS:B - all bodies

The value of 'n' being exactly 4 for "all bodies" is not accurate. The correct statement is that for all idealized bodies, specifically black bodies, the value of 'n' is exactly 4. A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. It also emits radiation at the maximum possible intensity for any given temperature, according to Planck's law. The Stefan-Boltzmann law states that the total rate of radiation emitted per unit surface area of a black body is directly proportional to the fourth power of the absolute temperature (T) of the body. Mathematically, this is expressed as: 4Q=σT4 Where:

  • Q is the total rate of radiation emitted per unit surface area,
  • σ is the Stefan-Boltzmann constant.
For black bodies, the exponent 'n' in Tn is exactly 4, according to the Stefan-Boltzmann law. This means that the total rate of radiation emitted by a black body is proportional to 4T4, where T is the absolute temperature of the body. However, for real-world objects that are not perfect black bodies, the value of 'n' can vary depending on factors such as surface properties, emissivity, and geometry. So, while the value of 'n' is 4 for black bodies, it may not hold true for all bodies. Different materials and surface conditions can lead to different values of 'n' in the expression for thermal radiation emitted by a body.