Specific Heat of Solids

Object: To determine the specific heat of a given solid specimen.

Theory: Thermal energy is an internal energy that consists of the kinetic and potential energies associated with the random motions of the atoms, molecules, and other microscopic bodies within an object. If there is an environment with temperature and a system with temperature , then the two will reach thermal equilibrium () if given enough time. The transfer energy is called heat and has the symbol . Heat is positive when absorbed and negative when lost. Heat is the energy that is transferred between a system and its environment because of the temperature difference that exists between them. The SI unit for heat is the Joule, . The British thermal, unit is defined as the amount of heat to raise of water from 63⁰ F to 64⁰ F. The calorie is defined as the amount of heat to raise the temperature of 1 gm of water 1⁰ C.

Heat capacity of an object is the proportionality constant between the heat and the temperature change.

Specific heat is defined as heat capacity per unit mass, C.

If we have two objects of different material and temperature, according to the conservation of energy then

is the mass of the metal solid, is the specific heat of the metal solid, and is the change in temperature of the solid. is the mass of the water,is the specific heat of the water, while is the change in temperature of the water.

Since the metal solid will be cooled and its final temperature will be less than its initial temperature we write as . Also, it is assumed that none of the heat is lost to the surroundings.

Apparatus: Double boiler, styrofoamcalorimeter, two temperature sensors (plugged into the computer interface), metal cylinder, metal cup with handle, and a mass-balance.

Procedure:

Fill the double-boiler approximately three-quarters full of water, and start heating it.

  1. Place 50 ml of water into the styrofoam calorimeter. (50 ml of water is equivalent to 50 grams of water, so = 50 grams)
  2. Put the temperature sensor into the Styrofoam calorimeter and monitor the computer until the temperature is stable this is (initial temperature of water).
  3. Weigh the metal cylinder and record . Place a metal cylinder inside a metal cup with handle along with water until the metal is half full. Then partially immerse the metal cup in water that is inside the boiler but donot warm it above approximately 96 to 98˚C, but please not above 98˚C. Record the stable temperature, .
  4. Move the metal cylinder from the metal cup with handle using the string provided and place the metal cylinder in the Styrofoam calorimeter and gently stir the water while keeping an eye on the thermometerand monitor the temperature. Record the highest temperature reached which is the final equilibrium temperature which will be which equals .
  5. Calculate the specific heat of the metal cylinder from the data and then compare it with the standard value to find the percentage error.
  6. Repeat the process for each of three metal cylinders indicated in the table below. Be SURE to use a new fresh cool 50 ml water sample for each metal cylinder experiment.

, specific heat
Material / /
Steel / 452 / 0.108
Aluminum / 900 / 0.215
Copper / 386 / 0.0923
Water / 4186 / 1

Question: What are the assumptions made in the experiment?

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