Originally the pan and water are not in thermal equilibrium: the pan is at a higher temperature than the water. The pan is placed on an insulated pad so that little heat transfer occurs with the surroundings. What is the temperature when the water and pan reach thermal equilibrium a short time later? Assume that the pan is placed on an insulated pad and that a negligible amount of water boils off. 0✬ water (about a cup) into a 0.500-kg aluminum pan off the stove with a temperature of 150✬ 150✬. Calculate the change in gravitational potential energy as the truck goes downhillĬalculating the Final Temperature When Heat Is Transferred Between Two Bodies: Pouring Cold Water in a Hot Pan.We first calculate the gravitational potential energy ( Mgh ) ( Mgh ) that the entire truck loses in its descent and then find the temperature increase produced in the brake material alone. When brakes are applied, gravitational potential energy is converted into internal energy of the brake material. If the brakes are not applied, gravitational potential energy is converted into kinetic energy. The problem is that the mass of the truck is large compared with that of the brake material absorbing the energy, and the temperature increase may occur too fast for sufficient heat to transfer from the brakes to the environment.Ĭalculate the temperature increase of 100 kg of brake material with an average specific heat of 800 J(kg☌) 800 J(kg☌) if the material retains 10% of the energy from a 10,000-kg truck descending 75.0 m (in vertical displacement) at a constant speed. This conversion prevents the gravitational potential energy from being converted into kinetic energy of the truck. Truck brakes used to control speed on a downhill run do work, converting gravitational potential energy into increased internal energy (higher temperature) of the brake material. In fact, water has one of the largest specific heats of any material, which is important for sustaining life on Earth.Ĭalculating the Temperature Increase from the Work Done on a Substance: Truck Brakes Overheat on Downhill Runs 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 14.1 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 ) ( Δ T ) is the same in units of kelvin and degrees Celsius. The specific heat c c is a property of the substance its SI unit is J/ ( kg ⋅ K ) 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. The symbol c c stands for specific heat and depends on the material and phase. ![]() Where Q Q is the symbol for heat transfer, m m is the mass of the substance, and Δ T 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 Q of heat to cause a temperature change Δ T 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 m, you need to add twice the heat. (a) The amount of heat transferred is directly proportional to the temperature change. Figure 14.4 The heat Q 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.
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