• Ajwrighter
In summary, a solid cylinder with radius r1 = 2.3 cm, length h1 = 4.2 cm, emissivity 0.88, and temperature 24°C is suspended in an environment of 55°C. The net thermal radiation transfer rate for this cylinder is 1.77W. When the cylinder is stretched to a radius of r2 = 0.52 cm, the ratio of its net thermal radiation transfer rate becomes 2.87 times the original rate. This is due to a mistake in the given equation, which should read (T^4 - Tenv^4) instead of (Tenv^4 - T^4). This has been confirmed by multiple sources.

#### Ajwrighter

1. A solid cylinder of radius r1 = 2.3 cm, length h1 = 4.2 cm, emissivity 0.88, and temperature 24°C is suspended in an environment of temperature 55°C. (a) What is the cylinder's net thermal radiation transfer rate P1? (b) If the cylinder is stretched until its radius is r2 = 0.52 cm, its net thermal radiation transfer rate becomes P2. What is the ratio P2/P1?
2. P1 = ($$\sigma$$) ($$\epsilon$$) A1(Tenv4 - T4)

A1 = 2($$\pi$$) r12 + 2 ($$\pi$$) r h

3. A1 = 9.393362*10-3m2
P1 = (5.67*10-8)(.88)(9.393362*10-3)((273+55)4-(273+24)4)) = 1.77W
I have (b) .. but for some reason (a) is wrong.. here is answer for (b) $$\frac{P2}{P1}$$ = 2.87
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Ok I just did it in mathmatica .. and it gave the same answer .. If
my intuition is incorrect then the only possible solution would be
that P1 is somehow =($$\sigma$$) ($$\epsilon$$) A1((24+273)4) ... but that's not how the question reads

I asked a friend he agrees with me.. but are we both wrong? not sure why the answer is considered wrong

had another person agree.. anyway I could get someone to review this problem and confirm?

any attempts?

ok I've resolved the problem. Both the book, and their online website have two distinct wrong equations to use.. The correct one would involve flipping the Tenv^4 with the T^4.. so it would read (T^4 - Tenv^4). So, I dub this problem as resolved in case anyone was interested.

## What is temperature?

Temperature is a measure of the average kinetic energy of the particles in a substance. It is commonly measured in degrees Celsius (°C) or Fahrenheit (°F).

## How is temperature related to thermal radiation transfer?

Temperature is one of the key factors that determine the rate of thermal radiation transfer. The higher the temperature of an object, the more thermal radiation it emits, and the faster it transfers heat to its surroundings.

## What is thermal radiation transfer?

Thermal radiation transfer is the process by which heat is transferred from one object to another through the emission and absorption of electromagnetic waves. This type of heat transfer does not require a medium and can occur in a vacuum.

## How does temperature affect the color of an object?

The temperature of an object affects its color through thermal radiation. As the temperature of an object increases, the wavelengths of thermal radiation it emits shift towards the visible spectrum, causing the object to appear to change color.

## Can temperature be measured accurately?

Yes, temperature can be measured accurately using various instruments such as thermometers, infrared cameras, and thermocouples. However, the accuracy of the measurement may be affected by factors such as the quality of the instrument and external conditions like air currents.