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Temperature Inside Hollow Sphere at given Radius between Inner and Outer Radius Formula

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Temperature is the degree or intensity of heat present in a substance or object. Check FAQs

T = T w + \frac{q G}{6 \cdot k} \cdot ({r 2}^{2} - r^{2}) + \frac{q G \cdot {r 1}^{3}}{3 \cdot k} \cdot (\frac{1}{r 2} - \frac{1}{r})

T - Temperature?T_w - Surface Temperature of Wall?q_G - Internal Heat Generation?k - Thermal Conductivity?r₂ - Outer Radius of Sphere?r - Radius?r₁ - Inner Radius of Sphere?

Temperature Inside Hollow Sphere at given Radius between Inner and Outer Radius Example

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Here is how the Temperature Inside Hollow Sphere at given Radius between Inner and Outer Radius equation looks like with Values.

Here is how the Temperature Inside Hollow Sphere at given Radius between Inner and Outer Radius equation looks like with Units.

Here is how the Temperature Inside Hollow Sphere at given Radius between Inner and Outer Radius equation looks like.

460 = 273 + \frac{100}{6 \cdot 10.18} \cdot (2^{2} - 4^{2}) + \frac{100 \cdot {6.32}^{3}}{3 \cdot 10.18} \cdot (\frac{1}{2} - \frac{1}{4})

460K = 273K + \frac{100W/m³}{6 \cdot 10.18W/(m*K)} \cdot ({2m}^{2} - {4m}^{2}) + \frac{100W/m³ \cdot {6.32m}^{3}}{3 \cdot 10.18W/(m*K)} \cdot (\frac{1}{2m} - \frac{1}{4m})

460 = 273 + \frac{100}{6 \cdot 10.18} \cdot (2^{2} - 4^{2}) + \frac{100 \cdot {6.32}^{3}}{3 \cdot 10.18} \cdot (\frac{1}{2} - \frac{1}{4})

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Temperature Inside Hollow Sphere at given Radius between Inner and Outer Radius Solution

Follow our step by step solution on how to calculate Temperature Inside Hollow Sphere at given Radius between Inner and Outer Radius?

FIRST Step Consider the formula

T = T w + \frac{q G}{6 \cdot k} \cdot ({r 2}^{2} - r^{2}) + \frac{q G \cdot {r 1}^{3}}{3 \cdot k} \cdot (\frac{1}{r 2} - \frac{1}{r})

Next Step Substitute values of Variables

∴

T = 273K + \frac{100W/m³}{6 \cdot 10.18W/(m*K)} \cdot ({2m}^{2} - {4m}^{2}) + \frac{100W/m³ \cdot {6.32m}^{3}}{3 \cdot 10.18W/(m*K)} \cdot (\frac{1}{2m} - \frac{1}{4m})

Next Step Prepare to Evaluate

∴

T = 273 + \frac{100}{6 \cdot 10.18} \cdot (2^{2} - 4^{2}) + \frac{100 \cdot {6.32}^{3}}{3 \cdot 10.18} \cdot (\frac{1}{2} - \frac{1}{4})

Next Step Evaluate

∴

T = 460.00000274085K

LAST Step Rounding Answer

∴

T = 460K

Temperature Inside Hollow Sphere at given Radius between Inner and Outer Radius Formula Elements

Variables

Temperature

Temperature is the degree or intensity of heat present in a substance or object.

Symbol: T

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Surface Temperature of Wall

Surface Temperature of wall is the temperature at or near a surface. Specifically, it may refer to as Surface air temperature, the temperature of the air near the surface of the earth.

Symbol: T_w

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Internal Heat Generation

Internal Heat Generation is defined as the conversion of electrical, chemical, or nuclear energy into heat (or thermal) energy which leads to a rise in temperature throughout the medium.

Symbol: q_G

Measurement: Power DensityUnit: W/m³