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A particular substance is being cooled b...

A particular substance is being cooled by a stream of cold air (temperature of the air is constant and is `5^(@)C`) where rate of cooling is directly proportional to square of difference of temperature of the substance and the air.
If the substance is cooled from `40^(@)C` to `30^(@)C` in 15 min and temperature after 1 hour is `T^(@)C,` then find the value of `[T]//2,` where [.] represents the greatest integer function.

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Knowledge Check

  • According to Newton's law, rate of cooling is proportional to the difference between the temperature of the body and the temperature of the air. If the temperature of the air is 20^(@)C and body cools for 20 min from 100^(@)C to 60^(@)C then the time it will take for it temperature to drop to 30^(@) is

    A
    30 min
    B
    40 min
    C
    60 min
    D
    80 min

  • A body cools from 50^@C " to " 40^@C in 5 min. If the temperature of the surrounding is 20^@C , the temperature of the body after the next 5 min would be

    A
    `36^@C`
    B
    `35^@C`
    C
    `33.33^@C`
    D
    `30^@C`

  • If a body cools down from 80^(@) C to 60^(@) C in 10 min when the temperature of the surrounding of the is 30^(@) C . Then, the temperature of the body after next 10 min will be

    A
    `50^(@) C`
    B
    `48^(@) C`
    C
    `30^(@) C`
    D
    None of the above

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