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Find out ratio of rate of loss of heat a...

Find out ratio of rate of loss of heat and rate of fall in temperature. (different body A cube, Sphere and Cylinder) (For Given Dimensions)

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To solve the problem of finding the ratio of the rate of loss of heat to the rate of fall in temperature for a cube, sphere, and cylinder, we will follow these steps: ### Step 1: Understand Newton's Law of Cooling According to Newton's Law of Cooling, the rate of heat loss (\( \frac{dq}{dt} \)) is proportional to the surface area (A) of the body and the temperature difference between the body and the surroundings. The formula can be expressed as: \[ \frac{dq}{dt} = -E \cdot A \cdot \sigma (T_b - T_s) \] Where: ...
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Rate Of Loss Heat

A solid aluminium sphere and a solid copper sphere of twice the radius are heated to the same temperature and are allowed to cool under identical surrounding temperatures. Assume that the emisssivity of both the spheres is the same. Find ratio of (a) the rate of heat loss from the aluminium sphere to the rate of all of temperature of tghe copper sphere. The specific heat copacity of aluminium =900Jkg^(-1) ^(@)C^(-1) . and that of copper =390Jkg^(-1) ^(@)C^(-1) . The denity of copper =3.4 times the correct wattage.

Knowledge Check

  • In the above question, the ratio of the initial rate of fall of temperature is

    A
    `((pi)/(6))^(1//3):1`
    B
    `1:1`
    C
    `((4pi)/(3))^(1//3):1`
    D
    `((3)/(4pi))^(2//3):1`

  • When a body of mass M loses heat, the rate of fall of temperature is proportional to

    A
    `M^(1//2)`
    B
    `M^(-1//2)`
    C
    M
    D
    `M^(-1)`

  • In the above problem the ratio of the initial rate of fall of the temperatures is nearly

    A
    2.49
    B
    3.11
    C
    1.99
    D
    24.9

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    A solid aluminium sphere and a solid copper sphere of twice the radius are heated to the same temperature and are allowed to cool under identical surrounding temperature. Assume that the emissivity of both the spheres is the same. Find the ratio of (a) the rate of heat from the aluminium sphere to the rate of heat loss from the copper sphere and (b) the rate of fall of temperature of the the aluminium sphere to the rate of fall temperature of teh copper sphere. The specific heat capacity of aluminium = 900 J//kg -^(@)C and that of copper = 390 J//kg-^(@)C . The density of copper is 3.4 times the density of aluminium.

    A solid cylinder and a sphere of same material are suspended in a room turn by turn, after heating them to the same temperature. The cylinder and the sphere have same radius and same surface area. (a) Find the ratio of initial rate of cooling of the sphere to that of the cylinder. (b) Will the ratio change if both the sphere and the cylinder are painted with a thin layer of lamp black?

    The relation between rate of loss of heat from the body and its absolute temperature is known as

    Rate of loss of heat of two spheres at same temperature having radii in ratio 1 : 2 is

    In previous problem, the ratio of the initial rates of cooling (i.e., rates of fall of temperature) is

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