### Specific Heat Capacity

 Fig. 3-1 When this swimming pool is filled with water, how much energy is required to rise the temperature of the water by 1oC?

You can easily heat up a kettle of water by putting it above flames. It would take more time if the kettle is full, because more energy is needed to heat up a larger amount of water. To heat up a kettle full of water, a stove in a kitchen will do, but imagine if you want to heat up all the water in a swimming pool, you would need a much larger source of energy. Thus the heat capacity of an object depends on its mass.

Suppose we are interested in knowing the energy that needs to raise temperature of 1 of water by 1 . This is a physical property specific to water; it doesn't matter if the kilogram of water is taken from a kettle, or from a large swimming pool. We call this quantity the specific heat capacity of water. The specific heat capacity of water is 4200 , meaning that it takes 4200 of energy to heat up 1 of water by 1 .

The specific heat capacity of a substance is denoted by the symbol . It then follows that the energy needed to heat up of that substance by a temperature of is given by

The specific heat capacity and the heat capacity of an object are thus related by

 Activity: Mixing hot and cold water

 Mixing hot and cold water. Play [Low | High]    Download [Low(92kb) | High(121kb)]

The following table gives the specific heat capacity of some common substances.

 Substance Specific heat capacity () Water 4200 Alcohol 2400 Sand 840 Granite 800 Ice 2100 Glass 670 Copper 390 Iron 460

Example

 Fig. 3-2 Experiment to find the specific heat capacity of water.

The apparatus shown in the figure is used to conduct an experiment on finding the specific heat capacity of water. The joulemeter records the heat energy supplied to the water by the immersion heater. The mass of water is measured by an electronic balance. When 12700 of energy is supplied to 100 of water, the rise in temperature is found to be 30 . Find the specific heat capacity of water.

Solution

Since

The specific heat capacity of water found in this experiment is 4230 .

The last example shows the standard method used in a school laboratory to measure the specific heat capacity of water. Now let's try another less accurate but more interesting method - use a domestic electric boiler to find the specific heat capacity of water. In fact, all apparatus used in this activity can be found in an ordinary family.

Example

 Fig. 3-3 What is temperature change of the hot water when it is poured into the cup?

When preparing instant cup noodle, Tommy pours 300 of water at 90 onto 75 of noodle at 20 in a polystyrene cup. Estimate the temperature of the mixture soon after mixing. Would the actual temperature be higher or lower than the estimated value? Why? Given the specific heat capacity of the noodle and water are 1700 and 4200 respectively.

Solution

Let be the temperature of the mixture soon after mixing.

Heat loss by hot water =

Heat gain by noodle =

Assuming no heat is lost to the surrounding, we have

Heat loss by hot water = Heat gain by noodle

The temperature of the mixture is 83.6 . We expect the actual temperature to be much lower than this value due to heat loss to the surrounding and the heat used to raise thetemperature of the polystyre ne cup.

Example

 Fig. 3-4 If the same amount of heat is supplied to sand and water of the same mass, which one would have a larger change in temperature?

The initial temperature of 0.1 of sand is 25 . If 840 of heat is transferred to it, what is the final temperature of the sand? Repeat the calculation with the same mass of water. Given the specific heat capacity of sand is 840 ; and the specific heat capacity of water is 4200 .

Solution

Consider the sand first. Since

we have

For the same mass of water, we have

The final temperature of the sand is 35 and the final temperature of the water is 27 . We can see that the change in temperature of water is much smaller than that of sand because water has a much higher specific heat capacity.

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