where Cv is the specific molar heat capacity at constant volume. where q is the specific heating rate (SI units: J kg–1 s–1). Note that if the volume is constant, we obtain the expression of the heating of a constant volume. where Cp is the heat capacity at constant pressure and cp is the specific heat capacity at constant pressure. This is difficult to say, as it is possible that the volume of the air parcel may change in addition to the temperature increase. So we could guess that at a fixed heating rate Q, the temperature increase in the open box is less than the temperature increase in the sealed box, where the volume is constant, because the volume can change as well as the temperature. CV, the constant that relates Q to temperature change, is called constant volume heat capacity. The heat capacity has units of J K-1. It is often useful to express these equations in specific quantities, such as specific volume (α ≡ V/m = ρ-1), specific heat at constant pressure (cp ≡ Cp/m) and specific heat at constant volume (cV ≡ CV/m). With these definitions, the first three equations above are given: If Q is an amount of heat needed to increase the n-mol temperature of a gas by (Delta T) at constant volume, the molar heat capacity of the gas Suppose the gas is heated with a constant volume and its temperature increases by dT, then the amount of heat, supplied to the system at a constant volume, All thermal energy supplied is used only to increase the internal energy and temperature of a gas. But in the case of constant pressure and here, all the thermal energy supplied is used to increase the internal energy and work against the external pressure.
Therefore, more heat is needed to increase the temperature of the gas when the gas is heated to the same temperature. Therefore, the specific heat of a gas at constant pressure is greater than the specific heat at constant volume, Cp > Cv., where Cp is the molar specific heat capacity at constant pressure. Since the heat supplied is used in two processes: (i) to increase internal energy, dU and (ii) for external work, dW. Then we have from the first law of thermodynamics Heat Capacity C is the amount of energy needed to increase the temperature of a substance by a certain amount. Thus, C = Q dT dt and has SI units of J/K. C depends on the substance itself, the mass of the substance and the conditions under which the energy is added. We will take into account two special conditions: constant volume and constant pressure. If dQ is the amount of heat observed by the system and dV is the increase in the internal energy of the system, then dW is the work that the system performs according to the first law of thermodynamics. Weather conditions include heating and cooling, rising air patches and falling rain, thunderstorms and snow, freezing and thawing.
All this time happens according to the three laws of thermodynamics. The first law of thermodynamics tells us how to explain energy in any molecular system, including the atmosphere. As we will see, the concept of temperature is closely related to the concept of energy, namely thermal energy, but they are not the same because there are other forms of energy that can be exchanged with thermal energy, such as mechanical energy or electrical energy. Each parcel of air contains molecules that have internal energy, which, thinking of the atmosphere, is only the kinetic energy of molecules (associated with molecular rotations and in some cases vibrations) and the potential energy of molecules (associated with the forces of attraction and repulsion between molecules). Internal energy does not take into account its chemical bonds or the nuclear energy of the nucleus, because these do not change during collisions between air molecules. Working on an air package involves either an expansion by increasing the volume or a downsizing. In the atmosphere, as in any system of molecules, energy is not created or destroyed, but conserved. We just need to track where the energy is coming from and where it is going. Consider a box with rigid walls and therefore a constant volume: dV dT = 0. No work is done and only the internal energy can change due to warming.
Consider the atmospheric surface layer, which is 100 m deep and has an average density of 1.2 kg m-3. The early morning sun warms the surface, which heats the air to a heating rate of F = 50 W m-2. How fast does the temperature in the layer increase? Why is this increase significant? The heat capacity, CV, depends on the mass and the type of material. We can therefore write CV as: Let U be the internal energy of an air parcel, Q the heating rate of this air parcel and W the speed at which the air parcel is worked. Next: Often we do not have a clearly defined volume, but only an air mass. We can easily measure the pressure and temperature of the air mass, but we cannot easily measure its volume.