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# 3.11: Temperature Changes: Heat Capacity

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If a swimming pool and wading pool, both full of water at the same temperature, were subjected to the same input of heat energy, the wading pool would certainly rise in temperature more quickly than the swimming pool. The heat capacity of an object depends on both its mass and its chemical composition. Because of its much larger mass, the swimming pool of water has a larger heat capacity than the wading pool.

## Heat Capacity and Specific Heat

Different substances respond to heat in different ways. If a metal chair sits in the bright sun on a hot day, it may become quite hot to the touch. An equal mass of water in the same sun will not become nearly as hot. We would say that water has a high heat capacity (the amount of heat required to raise the temperature of an object by $$1^\text{o} \text{C}$$). Water is very resistant to changes in temperature, while metals in general are not. The specific heat of a substance is the amount of energy required to raise the temperature of 1 gram of the substance by $$1^\text{o} \text{C}$$. The symbol for specific heat is $$c_p$$, with the $$p$$ subscript referring to the fact that specific heats are measured at constant pressure. The units for specific heat can either be joules per gram per degree $$\left( \text{J/g}^\text{o} \text{C} \right)$$ or calories per gram per degree $$\left( \text{cal/g}^\text{o} \text{C} \right)$$ (Table $$\PageIndex{1}$$). This text will use $$\text{J/g}^\text{o} \text{C}$$ for specific heat.

$\text{specific heat}= \dfrac{\text{heat}}{\text{mass} \times \text{cal/g}^\text{o} \text{C}}$

Notice that water has a very high specific heat compared to most other substances.

Table $$\PageIndex{1}$$: Specific Heat Capacities
Substance Specific Heat Capacity
at 25oC in J/g oC
Substance Specific Heat Capacity
at 25oC in J/g oC
$$\ce{H2}$$ gas 14.267
steam @ 100oC
2.010
$$\ce{He}$$ gas 5.300
vegetable oil
2.000
$$\ce{H2O(l)}$$ 4.184
sodium
1.23
lithium
3.56
air
1.020
ethyl alcohol
2.460
magnesium
1.020
ethylene glycol
2.200
aluminum
0.900
ice @ 0oC
2.010
concrete
0.880
steam @ 100oC
2.010
glass
0.840

Water is commonly used as a coolant for machinery because it is able to absorb large quantities of heat (see table above). Coastal climates are much more moderate than inland climates because of the presence of the ocean. Water in lakes or oceans absorbs heat from the air on hot days and releases it back into the air on cool days.

Figure $$\PageIndex{1}$$: This power plant in West Virginia, like many others, is located next to a large lake so that the water from the lake can be used as a coolant. Cool water from the lake is pumped into the plant, while warmer water is pumped out of the plant and back into the lake.

## Summary

• Heat capacity is the amount of heat required to raise the temperature of an object by $$1^\text{o} \text{C}$$).
• Thespecific heat of a substance is the amount of energy required to raise the temperature of 1 gram of the substance by $$1^\text{o} \text{C}$$.