Six wood stoves have total surface areas A and surface...

Six wood stoves have total surface areas $A$ and surface temperatures $T$ as given. Rank them in order of the power radiated, from greatest to least. Assume they all have the same emissivity. (a) $A=1.00 \mathrm{m}^{2}, T=227^{\circ} \mathrm{C}$ (b) $A=1.01 \mathrm{m}^{2}, T=227^{\circ} \mathrm{C}$ (c) $A=1.05 \mathrm{m}^{2}, T=227^{\circ} \mathrm{C}$ (d) $A=1.00 \mathrm{m}^{2}, T=232^{\circ} \mathrm{C}$ (e) $A=0.99 \mathrm{m}^{2}, T=232^{\circ} \mathrm{C}$ (f) $A=0.98 \mathrm{m}^{2}, T=232^{\circ} \mathrm{C}$

Six wood stoves have total surface areas $A$ and surface temperatures $T$ as given. Rank them in order of the power radiated, from greatest to least. Assume they all have the same emissivity.
(a) $A=1.00 \mathrm{m}^{2}, T=227^{\circ} \mathrm{C}$
(b) $A=1.01 \mathrm{m}^{2}, T=227^{\circ} \mathrm{C}$
(c) $A=1.05 \mathrm{m}^{2}, T=227^{\circ} \mathrm{C}$
(d) $A=1.00 \mathrm{m}^{2}, T=232^{\circ} \mathrm{C}$
(e) $A=0.99 \mathrm{m}^{2}, T=232^{\circ} \mathrm{C}$
(f) $A=0.98 \mathrm{m}^{2}, T=232^{\circ} \mathrm{C}$

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Key Concepts

Surface Area in Radiation

The total power radiated by an object is also directly proportional to its surface area. This means that when comparing objects at the same temperature, those with larger surface areas will radiate more energy.

Emissivity

Emissivity is a measure of how efficiently an object radiates energy compared to an ideal black body. When emissivity is constant across different objects, differences in radiated power can be attributed solely to differences in area and temperature.

Temperature Conversion

Physical laws such as the Stefan-Boltzmann law require temperatures to be expressed in Kelvin rather than Celsius. Converting Celsius to Kelvin (by adding 273.15) is essential for correct calculation of radiated power.

Stefan-Boltzmann Law

This law relates the power radiated by a black body to its temperature, stating that the power per unit area is proportional to the fourth power of its absolute temperature (in Kelvin). This means even small increases in temperature result in significant increases in radiated power.

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