In adiabatic expansion, the gas is expanded without gain of heat energy from the surroundings but in the expense of its own internal energy. Thus the internal energy of the gas decreases due to adiabatic expansion. The internal energy is a function of temperature. When the internal energy decreases, the temperature of the gas also decreases. Hence, the temperature of the gas drops in an adiabatic expansion.
The limitations of thermodynamics are:
(i) It does not indicate the direction of heat transfer.
(ii) It does not tell anything about the direction in which the process can or cannot proceed.
(iii) It does not indicate as to what extent the heat energy can be converted into mechanical work.
The specific heat capacity of the gas depends on the conditions under which heat is added. The gas can be heated at constant pressure and at constant volume. Therefore, specific heat of a gas is defined either at constant pressure or at constant volume and hence has two specific heats.
When gas is heated at constant volume, it cannot perform external work. Hence the heat supplied will increase the internal energy of the gas and thus the temperature. But when the gas is heated at constant pressure, the heat supplied will partly increase its internal energy (temperature) and partly will be utilized in performing external work. Therefore, it is clear that more heat is required to raise the temperature by 10C at constant pressure. Hence specific heat capacity of a gas at constant pressure is always greater than at constant volume.
Yes, heat can be considered as a form of potential energy. This can be illustrated with the example of melting of ice. During melting of ice, its temperature remains constant and hence its kinetic energy remains constant. The amount of heat energy absorbed by ice is used up in separating the molecules apart and it is stored in the form of potential energy. Thus heat is stored in the form of potential energy and hence can be considered as a form of potential energy.
Our internal body temperature in more than the surrounding. When we blow on the block of our hand with our mouth wide open, the hot air from the inner body comes out slowly. Since it is a slow process, it is an isothermal process and thus the temperature of the air blown remains constant. Hence we feel warm.
But when we blow with mouth partially closed, the hot air from the inner body comes out rapidly and expands out of the mouth. It is an adiabatic expansion. The temperature of the system decreases in adiabatic expansion. Hence the temperature of the air out of the mouth decreases and we feel cool.