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CH301 9b - The Measurement of Heat The amount of heat...

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1 Chapter 9b Thermodynamics: The First Law 2 The amount of heat energy needed to change the temperature of an object is known as the heat capacity. Heat capacity is an extensive property that requires more heat if the object is larger. The two objects are the same material, the larger object requires more heat to change the temperature that the smaller object. The Measurement of Heat 3 The Measurement of Heat Heat energy transferred to a system can be measured if the heat capacity (C) of the system is known. T heat q C = ) ( 4 Heat Capacities of Ideal Gases Internal energy is energy stored in a system as kinetic and potential energy. Kinetic energy is due to motion The faster a molecule travels, the greater its kinetic energy. When we heat a gas, the average speed of the molecules increases. When we do work on a gas in an insulated container, the molecules are also stimulated to move faster. The increase in the average speed of the gas molecules corresponds to an increase in the total kinetic energy of the molecules resulting in an increase in the internal energy of the gas. 5 Heat Capacities of Ideal Gases The average speed of gas molecules is an indication of temperature. Therefore, the increase in internal energy also corresponds to an increase in temperature. A system at high temperature has a greater internal energy than the same system at a lower temperature. 6 Heat Capacities of Ideal Gases An ideal gas, at high temperatures and low pressures, obey the ideal gas relationship PV = nR. For an ideal gas: (K.E.) avg = the average, random, translational energy for 1.0 mole of a gas at a given temperature. Translational kinetic energy is energy possessed by objects moving through space. Like speeding bullets, gas molecules have this energy of motion. ( ) 3 . . 2 avg K E RT =
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7 Heat Capacities of Ideal Gases The kinetic energy of an ideal gas can only be changed by changing the temperature. The heat energy required to change the energy of 1 mole of an ideal gas by changing temperature is: Therefore, if we change the temperature by 1 Kelvin (K), that is T = 1, the amount of heat energy required is 3/2 R. 3 2 Heat energy required R T = 8 Heat Capacities of Ideal Gases The molar heat capacity is the energy required to raise the temperature of 1 mole of a substance by 1 K. For an ideal gas, the molar heat capacity is: C v = molar heat capacity at constant volume. When a gas is heated in a rigid container in which no volume change can occur, V = 0, no PV work can be done. The heat energy that flows into the gas is used to increase the translational energies of the gas molecules. 3 2 v C R = 9 Heat Capacities of Ideal Gases When heating an ideal gas at constant pressure, its volume increases and PV work is done. Therefore, the heat energy required must provide energy to change the translational energy of the gas and must also provide energy to allow work to be done.
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