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A 500W lamp loses all of its energy by e...

A 500W lamp loses all of its energy by emission of radiation from the surface. If the area of the surface of the filament is `2.0cm^(2)` and its emissivity is 0.5, estimate the temperature of its filameiit. Given that Stefan constant, ` sigma =5.7xx10^(-8)W//m^(2)K^(4).` Neglect radiation receivedby lamp from surrounding.

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AI Generated Solution

To solve the problem, we will use Stefan-Boltzmann's law, which states that the power radiated by a black body is proportional to the fourth power of its absolute temperature. The formula is given by: \[ P = \sigma \cdot \epsilon \cdot A \cdot T^4 \] Where: - \( P \) = Power radiated (W) - \( \sigma \) = Stefan-Boltzmann constant (\( 5.7 \times 10^{-8} \, \text{W/m}^2\text{K}^4 \)) - \( \epsilon \) = Emissivity of the surface (dimensionless) ...
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A 300 W lamp loses all its energy by emission of radiation from the surface of its filament. If the area of surface of filament is 2.4cm^(2) and is of emissivity 0.4, estimate its temperature. Given that sigma = 1.36 xx 10^(-12) cal cm^(-2) s^(-1) K^(-4) J=4.2 J cal^(-1) . Neglect the absorption from the surroundings.

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Knowledge Check

  • A body having a surface area of 50cm^2 radiates 300J of energy per minute at a temperature of 727^(@)C . The emissivity of the body is ( Stefan's constant =5.67xx10^(-8)W//m^2K^4 )

    A
    0.09
    B
    0.018
    C
    0.36
    D
    0.54

  • The surface of a black body is at a tempera ture 727^(@)C and its cross section is 1m^(2) Heat radi ated from this surface in one minute in Joules is (Stefan's constant =5.7 xx 10^(-8) W//m^(2)//k^(4)) .

    A
    `34.2xx10^(5)`
    B
    `2.5xx10^(5)`
    C
    `3.42xx10^(5)`
    D
    `2.5xx10^(6)`

  • Calculate the temperature at which a perfect black body radiates at the rate of 1 W cm^(-2) , value of Stefan's constant, sigma = 5.67 xx 10^(-8) W m^(-2)K^(-4)

    A
    576 K
    B
    648 K
    C
    695 K
    D
    766 K

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    The operating temperature of a tungesten filament in an indandescent lamp is 2000 K and its emissivity is 0.3 . Find the surface area of the filament of a 25 watt lamp. Stefan's constant sigma = 5.67xx10^(-8) Wm^(-2)K^(-4)

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