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The pan and the water are always at the same temperature. (a) How much heat is required? What percentage of the heat is used to raise the temperature of (b) the pan and (c) the water? Strategy Calculating the Required Heat: Heating Water in an Aluminum PanĪ 0.500 kg aluminum pan on a stove is used to heat 0.250 liters of water from 20.0✬ to 80.0✬. In fact, water has one of the largest specific heats of any material, which is important for sustaining life on Earth.Įxample 1. We see from this table that the specific heat of water is five times that of glass and ten times that of iron, which means that it takes five times as much heat to raise the temperature of water the same amount as for glass and ten times as much heat to raise the temperature of water as for iron. Except for gases, the temperature and volume dependence of the specific heat of most substances is weak. Table 1 lists representative values of specific heat for various substances. In general, the specific heat also depends on the temperature. Values of specific heat must generally be looked up in tables, because there is no simple way to calculate them.

If heat transfer is measured in kilocalories, then the unit of specific heat is kcal/(kg ⋅ ✬). Recall that the temperature change (Δ T) is the same in units of kelvin and degrees Celsius. The specific heat c is a property of the substance its SI unit is J/(kg ⋅ K) or J/(kg ⋅ ✬). The specific heat is the amount of heat necessary to change the temperature of 1.00 kg of mass by 1.00✬. The symbol c stands for specific heat and depends on the material and phase. The quantitative relationship between heat transfer and temperature change contains all three factors: Q = mcΔ T, where Q is the symbol for heat transfer, m is the mass of the substance, and Δ T is the change in temperature. For the same substance, the transferred heat also depends on the phase (gas, liquid, or solid). The transferred heat also depends on the substance so that, for example, the heat necessary to raise the temperature is less for alcohol than for water. Owing to the fact that the transferred heat is equal to the change in the internal energy, the heat is proportional to the mass of the substance and the temperature change. Owing to the fact that the (average) kinetic energy of an atom or molecule is proportional to the absolute temperature, the internal energy of a system is proportional to the absolute temperature and the number of atoms or molecules. The dependence on temperature change and mass are easily understood. If it takes an amount Q of heat to cause a temperature change Δ T in a given mass of copper, it will take 10.8 times that amount of heat to cause the equivalent temperature change in the same mass of water assuming no phase change in either substance. (c) The amount of heat transferred depends on the substance and its phase. To cause an equivalent temperature change in a doubled mass, you need to add twice the heat. (b) The amount of heat transferred is also directly proportional to the mass. To double the temperature change of a mass m, you need to add twice the heat. (a) The amount of heat transferred is directly proportional to the temperature change. The heat Q transferred to cause a temperature change depends on the magnitude of the temperature change, the mass of the system, and the substance and phase involved. Every time, onĪverage, x increased 1, y went down by negative 2.Figure 1. Rate of change of y of x over the interval from This right over here, negative 6 over 3 is the So when we increased x byģ, we decreased y of x by 6. We are at negative 5, and we go up to negative 2. Higher up on the list, let's call this the start. So let's say that weĬan kind of view this as our endpoint right over here.

Over this interval? So y went from a 6 to a 0. Change in y overĪverage rate of change over this interval. Make that a little bit neater- this is going toīe the change in y of x over that interval over theĬhange of x of that interval. So to figure out theĪverage rate of change, so the average rateĪnd we can assume it's with respect to x- let me

And when x is equal to negativeĢ, y of x is equal to 0. When x is equal to negativeĥ, y of x is equal to 6.