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Once we have a thermometer, we can easily show that heating an object causes its temperature to rise. Perhaps then temperature is the same thing as heat. Let’s test this idea and measure the temperature rise produced by a simple heat-producing chemical reaction like burning methane. As an example, we burn 1.0 g of methane gas and use the heat released to raise the temperature of 1.000 kg of water (essentially 1.0 L of water). We observe that the water temperature rises by exactly 13.3 °C. This result is constant for this experiment. By performing this experiment repeatedly, we always find that the temperature of this quantity of water increases by 13.3 °C. Therefore, the same quantity of heat must always be produced by reaction of this quantity of methane. As such, it is very tempting to say that the amount of heat released by burning 1.0 g of methane is 13.3 °C. If this is true, then every time 1.0 g of methane is burned, a temperature rise of 13.3 °C should be observed.
However, if we burn 1.0 g of methane to heat 500 g of water instead, we observe a temperature rise of 26.6 °C. And if we burn 1.0 g of methane to heat 1.000 kg of iron, we observe a temperature rise of 123 °C. Therefore, the temperature rise observed depends on the quantity of material heated as well as what the substance is that is heated. Our temptation has led us astray. 13.3 °C is not an appropriate measure of this quantity of heat, since we cannot say that the burning of 1.0 g of methane "produces 13.3 °C of heat." Such a statement is clearly nonsense, so we must keep the concepts of temperature and heat distinct.
Although temperature and heat are not the same concept, our data do tell us that they are related somehow. Let’s look at some additional data. We know that if we burn 1.0 g of methane, the temperature rise in 1.0 kg of water is 13.3 °C or the temperature rise for 0.5 kg of water is 26.6 °C. What if we burn 2.0 g of methane? Experimentally, the temperature rise in 1.0 kg of water is 26.6 °C or the temperature rise for 0.5 kg of water is 53.2 °C. Look at those data carefully. We can reasonably assume that burning twice as much methane generates twice as much heat. And we see that it produces twice the temperature change of a fixed amount of water. This tells us that the temperature change for a fixed amount of water is proportional to the heat absorbed by the water.
Does this work for other materials? Earlier, we used the heat from burning 1.0 g of methane to heat 1.0 kg of iron, and we saw a temperature increase of 123 °C. If we burn 2.0 g of methane to heat 1.0 kg of iron, the temperature increase is found to double to 246 °C. Again, the temperature change is proportional to the heat absorbed. Let’s put this in symbols. If we call the quantity of heat q, and ΔT is the temperature rise produced by this heat, then we have observed that
where C is a proportionality constant. We need to be careful with this equation, though, because our data say that the relationship between q and ΔT depends on what material is heated (water or iron) and how much is heated (1.0 kg or 0.5 kg). So C depends on these same things: what material is heated and how much of the material is there. C is therefore a property of each material and is called the “heat capacity” of the material.
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