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In lab you submerge 100 g of 41 degree Celcius iron nails in 100 g of 25 degree Celcius water (the specific heat of iron is 0.12 cal/g degrees Celcius)
A)Equate the heat gained by the water to the heat lost by the nails and find the final temperature of the water.
B)Your lab partner is surprised by the result and says that since the masses of iron and water are equal, the final water temperature should lie closer to 33 degrees Celcius, half-way between. What is your explanation?

  • physics -

    Heat gained = Heat loss

    Let final temperature be x,

    Specific heat of Iron:
    0.12 cal/g°C = 502 J/kg °C


    Specific Heat of Water: 4186 J/kg °C

    Heat gained by water = mass x specific heat capacity x change in temperature
    =100(4186)* (x-25)
    =(418600x-10465000)J

    Heat lost by nails = mass x specific heat capacity x change in temperature
    =100(502)x (41-x)
    =(2058200-50200x)J

    Therefore:
    418600x + 50200x= 2058200+10465000
    468800x = 12523200
    x= 27.7 °C

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