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9.3: Specific Heat

  • Page ID
    2827
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    Beehive Geyser in Yellowstone National Park
    Figure 9.3.1

    This image is of the Beehive Geyser in Yellowstone National Park. Underground water is heated by the earth’s molten core and, when sufficient pressure is built up, the water shoots out of the ground in an amazing display.

    Specific Heat

    When heat flows into an object, its thermal energy increases and so does its temperature. The amount of temperature increase depends on three things: 1) how much heat was added, 2) the size of the object, and 3) the material of which the object is made. When you add the same amount of heat to the same mass of different substances, the amount of temperature increase is different. Each substance has a specific heat, which is the amount of heat necessary to raise one mass unit of that substance by one temperature unit.

    In the SI system, specific heat is measured in J/kg•K. (Occasionally, you may also see specific heat expressed sometimes in J/g•K). The specific heat of aluminum is 903 J/kg•K. Therefore, it requires 903 J to raise 1.00 kg of aluminum by 1.00 K.

    Specific Heat of Some Common Substances
    Material Specific Heat (J/kg•K)
    Aluminum 903
    Brass 376
    Carbon 710
    Copper 385
    Glass 664
    Ice 2060
    Lead 130
    Methanol 2450
    Water Vapor 2020
    Water (liquid) 4180
    Zinc 388

    The amount of heat gained or lost by an object when its temperature changes can be calculated by the formula

    Q=mcΔt,

    where Q is the heat gained or lost, m is the mass of the object, c is its specific heat, and Δt is the change in temperature. You should note that the size of a Celsius degree and a Kelvin degree are exactly the same, and therefore Δt is the same whether measured in Celsius or Kelvin.

    Examples

    Example 9.3.1

    A 0.500 kg block of zinc is heated from 295 K to 350. K. How much heat was absorbed by the zinc?

    Solution

    Q=mcΔt=(0.500 kg)(388 J/kg⋅K)(350. K−295 K)=10,600 J

    Example 9.3.2

    845 J of heat are added to a 0.200 kg block of aluminum at a temperature of 312.00 K. How high will the temperature of the aluminum rise?

    Solution

    (t2−t1)=Qmc=845 J(0.200 kg)(903 J/kg⋅K)=4.68 K

    t2=t1+4.68 K=312.00 K+4.68 K=316.68 K

    Try to determine the identity of each unknown substance using specific heat in the PLIX Interactive below:

    Interactive Element

    Summary

    • When heat flows into an object, its thermal energy increases and so does its temperature.
    • The amount of temperature increase depends on three things: 1) how much heat was added, 2) the size of the object, and 3) the material of which the object is made.
    • Each substance has a specific heat, which is the amount of heat necessary to raise one mass unit of that substance by one temperature unit.
    • The amount of heat gained or lost by an object when its temperature changes can be calculated by the formula Q=mcΔt.

    Review

    1. How much heat is absorbed by 60.0 g of copper when it is heated from 20.0°C to 80.0°C?
    2. A 40.0 kg block of lead is heated from -25°C to 200.°C. How much heat is absorbed by the lead block?
    3. The cooling system of an automobile motor contains 20.0 kg of water. What is the Δt of the water if the engine operates until 836,000 J of heat have been added to the water?

    Additional Resources

    PLIX: Play, Learn, Interact, eXplore: Heat Chamber

    Real World Application: Some Of The Nicest Weather in California

    Videos: Specific Heat and Heat Capacity - Overview

    Study Guide: Thermal Properties Study Guide


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