Temperature and Heat

Specific heat, c = heat needed to warm 1 gram of material by 1 C°.

Equation

Q  =  c * m * ΔT

3.8

Heat Capacity

Various materials have different heat-holding capacities, as you have probably experienced from eating. A piece of pie recently taken from the oven may have a pleasantly warm crust but a mouth-burning cherry filling! Clearly cherries and their liquid hold thermal energy much longer than pie dough. I need a drink of water just thinking about it, maybe a piece of pie, too.

Definition: The specific heat, c, of a substance is the amount of heat needed to change 1 g of the substance by 1 C°.

Here are some values of specific heat for common materials (but not pie dough).

Specific heat is given in calories for mass in grams and Joules for kg.

Physics allow us to calculate how much heat, Q, is absorbed or released when the temperature of a substance changes:

heat = specific heat x mass x change in temperature Q  =  c * m * ΔT

For example, how much heat has to be added to increase the temperature of 100 g of copper by 20 C°?

Q = 0.09 * 100 g * 20 C° = 180 calories

One way to think of specific heat is how rapidly heat can be added to or lost from a substance compared to water. Copper gains heat about 10 times faster than water and it also loses heat ten times faster; copper is a good conductor of heat; water holds on to its internal energy.

Water’s unusually high specific heat makes an important difference in the warmth of the Earth’s surface. During spring and early summer the ocean is slow to warm because of its high specific heat, but by the end of summer it has absorbed a lot of thermal energy and cools slower than the nearby land, which has a lower specific heat. The loss of heat from the water warms the air and land for weeks after seasonal cooling has set in. The same thing happens each day during the winter, with warmed air blowing inland off the ocean. Living in a desert the air temperature falls abruptly after sunset for there is no large mass of water to release heat into the evening air. The planet Mars is entirely a desert so that the air temperature there plummets as the Sun sets.

Mars Temperatures

Temperature data for 20 Martian days (sols) measured by the Viking Lander, and Hubble Space Telescope image of Mars. Note the nightly temperature drop of typically 50 degrees!

Weird Water

Things expand when heated and contract when cooled. Water does, too, except when its temperature is near freezing. When water is cooled from room temperature (about 20°C) towards freezing its volume continuously decreases (and its density increases) until it reaches 4°C. At cooler temperatures the volume increases. This is because when water freezes it forms an open structure due to the angle its two hydrogen atoms attach to oxygen, increasing its volume by about 9%. But its mass does not change, so its density (remember density = mass/volume) decreases. That is why ice floats – it is less dense than water. The small difference in density between water and ice is also why about 7/8ths of an iceberg’s mass is below the sea surface. Ships have to be very careful of icebergs because they are often wider below sea level than they are above. The Titanic wasn’t careful enough in 1912.

Left: Iceberg, no source

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