### Specific Heat Capacity: Heating Up

#### Purposes

• To determine the specific heat capacity of various substances
• To potentially identify materials by their specific heat capacity

#### Set Up

Obtain a thermometer, two styrofoam cups, and an object.  Some of the objects which are using might include

```nut            coral      silver cylinder
fishing mass   basalt     pair of brown cylinders
golden cube    grey cube  dented cube w/ square handle```

#### Measurements

 Description of object: _________________ The mass of the styrofoam cup mc __________ The mass of the styrofoam cup with water mc+w __________ The mass of the water mc+w - mc mw __________ The mass of the object mx __________ The start temperature of the object tx __________ The start temperature of the water ti __________ The highest final temperature of the water and object tf __________

#### Procedure

1. Put the object in the boiling water.
2. Return water to boil.
3. Wait two minutes.
4. Rapidly transfer the object to the cup with water.
5. Cap the cup with the second cup and water and watch the temperature rise.
6. Record the highest temperature reached by the object and the water in the table above.

#### Calculations

Note that the specific heat capacity of water, cw, is 1 calorie/(gram ·°C)

First law of thermodynamics: Energy is conserved. Heat is conserved. The object cooled down. The water warmed up. The object lost heat. The water gained heat. The heat lost by the object to the water is equal to the heat gained by the water. Heat is measured in calories. The letter Q is used for heat in calories.

Qlost by object = Qgained by water

mxcx[tx - tf] = mwcw[tf-ti]

```(  mx  )cx[tx -(  tf  )] =( mw  )(cw)[( tf    )-(    ti    )]
(      )cx[tx -(      )] =(     )(1)[(       )-(          )]
```

Solve for cx, the specific heat capacity of the object.

cx = ___________

After performing the experiment on one material, obtain a second material by trading objects with another group.  Make the same basic measurements, calculations, and report the result.

 Description of second object: _________________ The mass of the styrofoam cup mc __________ The mass of the styrofoam cup with water mc+w __________ The mass of the water mc+w - mc mw __________ The mass of the object mx __________ The start temperature of the object tx __________ The start temperature of the water ti __________ The highest final temperature of the water and object tf __________
```(  mx  )cx[tx -(  tf  )] =( mw  )(cw)[( tf    )-(    ti    )]
(      )cx[tx -(      )] =(     )(1)[(       )-(          )]```

cx = ___________

Use the following table, if appropriate, to make an educated guess as to the materials you were working with if you were working with a metal. You can use density to guide you when in doubt.  The density is the mass divided by the volume. The volume of a cube is length×width×height, the volume of a cylinder is p×(radius)2×Length

material s.h.c. in cal/(g ·°C) Density g/cm3
aluminum 0.215 2.7
basalt 0.24*
brass 0.092 8.4
copper 0.092 8.96
glass, crown 0.161 2.5
iron 0.107 7.87