How much energy does a bar of iron radiate after losing 8.0 × 10^6J?

In summary, the bar of iron has dimensions of 0.5m x 0.2m x 0.1m, a volume of 1.0 × 10−2m3, and a surface area of 3.4 × 10−1m2. Its density is 7900 kg m3, heat capacity is 400 J kg◦C, and coefficient of linear expansion is 1.2 × 10−5. The bar is initially at 600K and has an emissivity of 0.8. After losing 8.0 × 106J of energy, the rate at which it radiates energy is 220 W. To calculate this, one would need
  • #1
physics123
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A bar of iron is 0.5m long, 0.2m wide and 0.1m high (which means its volume is 1.0 × 10−2m3 and its surface area is 3.4 × 10−1m2 ). Iron has a density of 7900 kg m3 , a heat capacity of 400 J kg◦C , and a coefficient of linear expansion of 1.2 × 10−5 . The bar of iron is initially at 600K.

Assuming that the emissivity e = 0.8, what is the rate at which iron radiates energy after it has lost 8.0 × 106J?I know the answer is 220 W, but how do I get that answer? Thanks!
 
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  • #2
physics123 said:
A bar of iron is 0.5m long, 0.2m wide and 0.1m high (which means its volume is 1.0 × 10−2m3 and its surface area is 3.4 × 10−1m2 ). Iron has a density of 7900 kg m3 , a heat capacity of 400 J kg◦C , and a coefficient of linear expansion of 1.2 × 10−5 . The bar of iron is initially at 600K.

Assuming that the emissivity e = 0.8, what is the rate at which iron radiates energy after it has lost 8.0 × 106J?I know the answer is 220 W, but how do I get that answer? Thanks!
A thorough analysis would consider the uneven temperature distribution that would develop within the bar as it cools. It involves Fourier transforms. I shall guess you are not expected to allow for that.
What would be the temperature drop in losing that much energy?
 
  • #3
Hint: Figure temperature after cooling, then go with Stefan-Boltzmann law, appropriately scaled. I would ignore the expansion coeff. - but, whatever.
 

1. What is heat transfer?

Heat transfer is the movement of thermal energy from one object to another due to a temperature difference. This can occur through three mechanisms: conduction, convection, and radiation.

2. What is radiation?

Radiation is the transfer of thermal energy through electromagnetic waves. Unlike conduction and convection, radiation does not require a medium to transfer heat.

3. How does heat transfer occur through radiation?

Radiation occurs when an object with a higher temperature emits electromagnetic waves, which are then absorbed by an object with a lower temperature. This causes the lower temperature object to increase in temperature.

4. What factors affect heat transfer through radiation?

The amount of heat transferred through radiation is influenced by the temperature difference between objects, the surface area of the objects, and the type of materials the objects are made of. Darker and rougher surfaces tend to emit and absorb more radiation compared to lighter and smoother surfaces.

5. How is radiation used in everyday life?

Radiation is used in a variety of everyday applications, such as cooking food in a microwave, heating a room with a space heater, and generating electricity through solar panels. It is also used in medical treatments, such as radiation therapy for cancer patients.

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