How does heat capacity change with temperature

Calculate the mass of water. Compare the percentage of heat going into the pan versus that going into the water. First, find the total transferred heat:. In this example, the heat transferred to the container is a significant fraction of the total transferred heat. Although the mass of the pan is twice that of the water, the specific heat of water is over four times greater than that of aluminum.

Therefore, it takes a bit more than twice the heat to achieve the given temperature change for the water as compared to the aluminum pan. Figure 2. The smoking brakes on this truck are a visible evidence of the mechanical equivalent of heat. 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. This conversion prevents the gravitational potential energy from being converted into kinetic energy of the truck.

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. If the brakes are not applied, gravitational potential energy is converted into kinetic energy. When brakes are applied, gravitational potential energy is converted into internal energy of the brake material.

We first calculate the gravitational potential energy Mgh that the entire truck loses in its descent and then find the temperature increase produced in the brake material alone. This temperature is close to the boiling point of water. If the truck had been traveling for some time, then just before the descent, the brake temperature would likely be higher than the ambient temperature.

The temperature increase in the descent would likely raise the temperature of the brake material above the boiling point of water, so this technique is not practical. However, the same idea underlies the recent hybrid technology of cars, where mechanical energy gravitational potential energy is converted by the brakes into electrical energy battery.

Note that Example 2 is an illustration of the mechanical equivalent of heat. Alternatively, the temperature increase could be produced by a blow torch instead of mechanically. Suppose you pour 0. Assume that the pan is placed on an insulated pad and that a negligible amount of water boils off. What is the temperature when the water and pan reach thermal equilibrium a short time later? The pan is placed on an insulated pad so that little heat transfer occurs with the surroundings.

Originally the pan and water are not in thermal equilibrium: the pan is at a higher temperature than the water. Heat transfer then restores thermal equilibrium once the water and pan are in contact. Because heat transfer between the pan and water takes place rapidly, the mass of evaporated water is negligible and the magnitude of the heat lost by the pan is equal to the heat gained by the water.

The exchange of heat stops once a thermal equilibrium between the pan and the water is achieved. Statistical thermodynamics posits that the fraction of the molecules that are in the lowest energy level approaches one as the temperature goes to zero.

If nearly all of the molecules are already in the lowest energy level, decreasing the temperature still further has a negligible effect on the energy and enthalpy of the system.

Given such heat capacity data, we can find the enthalpy or entropy change that occurs as we change the temperature of a quantity of the substance from some reference temperature to any other value.

When we use pressure and temperature as the independent variables, we have. At low temperatures, collisions do not provide enough energy to get out of the ground states for rotation or vibration. How does specific heat change with temperature? Chemistry Thermochemistry Specific Heat.

Ernest Z. Feb 19, Explanation: Specific heat is a measure of the ability of the substance to absorb heat. The heat goes first into increasing the kinetic energies of the molecules. If yes, why is it so? The heat capacity is the slope of the plot of internal energy U with temperature T.

The internal energy is energy that due to the rotation and vibrational energy a molecule possesses and as the temperature increases more rotational and vibrational energy levels becomes excited and so the internal energy increases. Initially the internal energy is small and changes slowly as energy is added, mainly because there is not enough energy to excite many rotations or vibrations.

Thus the slope of U vs. T is small and so is the heat capacity. At very high temperatures many, many energy levels are populated and so the rate of increase becomes constant as the temperature increases and so the heat capacity becomes constant, i. The plot shows the change of heat capacity with energy just for vibrational levels, but it has the same general shape when rotational and translational energy are added.

The 'bumpy' plot is due to the discrete values of vibrational energy levels. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.