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Quantity of heat gained by 100 kg of iro...

Quantity of heat gained by 100 kg of iron in raising its temperature by `10^(@)C` is `11xx10^(4)cal`. If a heater can supply heat at the rate of 1000 J `s^(-1)`, how much time does it take to heat an iron block of mass 2.5 kg when the mecury level in a Fahrenheit thermometer rises by 45 divisions.

Text Solution

Verified by Experts

Find the mass of the iron from given data.
Find the amount of heat gained by iron to raise its temperature by `10^(@)C` from the given data.
Find the specific heat of the iron from the formula, `Q=msDeltatheta`.
Find the corresponding temperature change in Celsius scale, when there is temperature change of 45 divisions in Fahrenheit scale from the formula
`(DeltaC)/(100)=(DeltaF)/(180)" "(1)`
Find how much amount of heat energy Q. is required for 2.5 kg iron block to increase its temperature by `.DeltaC`.
Make use of `Q.=2.5xxsxxDeltaC" "(2)`
Check the units of Q..
If it is in calorie, convert it into joule.
Then, find the amount of time taken to produce Q by dividing Q. by 1000.
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A block is kept in a room which is at 20^(@)C . To raise the temperature of the block, heat is given to it at a constant rate of 600 watt (using an electric heater). The temperature of the block rises with time as shown in the graph. The slope of the graph at time t = 0 is 3^(@)C s^(-1) . Once the temperature rises to 60^(@)C , the heater is switched off and another heater is switched on to maintain the temperature of the block at 60^(@)C . This new heater supplies heat at a constant rate of 100 watt. Assume that heat capacity of the block remains constant for the range of temperature involved. (a) Explain why the slope of the given graph is decreasing with time. (b) Calculate the heat capacity of the block. (c) If the 100 W heater is also switched off, what will be initial rate of cooling of the block? (d) Assuming that rate of heat loss by the block to the surrounding is proportional to difference in its temperature with surrounding, calculate the heat radiated per second by the block when it was at 30^(@)C .

50 gm of copper is heated to increase its temperature by 10^(@)C. If the same quantity of heat is given to 10 gm of water, the rise in its temperature is (Specific heat of copper =420 Joule-kg^(-1)@C^(-1)

Knowledge Check

  • 50 g of copper is heated to increase its temperature by 10^@C . If the same quantity of heat is given to 10g of water, the rise in its temperature is (specific heat of copper =420J//kg^(@)//C )

    A
    `5^@C`
    B
    `6^@C`
    C
    `7^@C`
    D
    `8^@C`

  • A 10.0 kg block of ice has a temperature of -10.0^(@)C . The pressure is one atmosphere. The block absorbs 4.11 xx 10^(6)J of heat. What is the final temperature of the liquid water ?

    A
    `0.58^(@)C`
    B
    `4.6^(@)C`
    C
    `9.2^(@)C`
    D
    `13^(@)C`

  • A 2.00 kg metal object requires 5.02 xx 10^(3) J of heat to raise its temperature from 20.0^(@)C to 40.0^(@)C . What is the specific heat capacity of the metal ?

    A
    `63.0J //( kg. ""^(@)C )`
    B
    `126J //(kg. ""^(@)C )`
    C
    `251 J //( kg. ""^(@)C )`
    D
    `502 J // ( kg . ""^(@ )C)`

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