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Special points of emphasis

Heat and Temperature


While we are at it, let us take a moment to appreciate the importance of water as the 'measure of all things'. Many units of measurement depend on the inherent qualities of water for their physical basis. For example, the density of water (1000kg/m3 or 1g/cm3) was used to translate an established unit of length (meter) into a unit of mass (kilogram). In other words, water is the cross-road for length and mass in the S.I. system. Furthermore, a fundamental thermodynamic quantity in chemistry, the calorie, was originally defined as the quantity of heat required to raise the temperature of one gram of water by 1 oC. The joule, though, has superseded the calorie as the standard unit of heat for scientific calculations. The joule is a mechanically defined unit of energy that does not specifically depend on the properties of water.

Heat and Temperature

The Ideal Gas and Kinetic Theory


Try to get past the simple definition of molar heat capacity to understand what it tells you about the ways that the particles of a substance can move to hold kinetic energy. In general, the more ways the molecules of a substance can move, whether in a line, rotating, or vibrating, the greater the molar heat capacity will be. The molar heat capacity reflects how many translational, rotational and vibrational modes a substance has available to store energy. The more places a substance has to put the energy, the greater the molar heat capacity.

The rule of Dulong and Petit is an example of this principle; the molar heat capacity of most solid metals is very nearly the same. The fact that some metals have atoms much larger than others does not matter for molar heat capacity. In a solid metal, the individual metal atoms occupy crystalline structures that allow for kinetic energy to exist in a similar way, so as heat flows in, for example, the amount of temperature change per mole of particles is the same for different metals (about 26 J/mol oC)

Heat and Temperature

The First Law of Thermodynamics

One facet of the discussion of heat capacity provides a good example of a somewhat tricky point that has appeared occasionally in MCAT passages dealing with thermodynamics. In general, heat capacities, whether specific heat or molar heat capacity, describe the relationship for particular substances between heat flow and temperature change. In the First Law of Thermodynamics, we will be discussing the centrally important principle that heat flowing into a system will either change its internal energy or be used to perform work. A distinction can therefore arise in the discussion of heat capacities regarding whether or not the heat capacity describes a gas at constant volume versus one at constant pressure. At constant volume, no thermodynamic work can be performed, but, at constant pressure, work definitely must be performed, because, to maintain constant pressure, the system must be expanding as heat flows in. For this reason, the heat capacity of gases is higher at constant pressure than constant volume. More heat will flow in at constant pressure before a given temperature change occurs because the system will necessarilly be simultaneously expending energy in the work of expanding its volume.

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