# Relationship between specific heat and equilibrium temperature

### Heat and temperature (article) | Khan Academy The specific heat is the amount of heat necessary to change the temperature of kg of mass by ºC. . Whenever there is a temperature difference, heat transfer occurs. .. object, and so-forth, until the objects are in thermal equilibrium. In the process of reaching thermal equilibrium, heat is transferred from one body to Heat flow is a results of a temperature difference between two bodies, and the In order to determine the heat capacity of a substance we not only need to. The quantitative relationship between heat transfer and temperature change . What is the temperature when the water and pan reach thermal equilibrium a.

### An Explanation of Thermal Equilibrium and its Formulas With Examples

During the initial study of thermodynamics scientists found that heat energy obtained from burning coal in steam engine could not be fully converted to mechanical work. Hence, they began studying about the energy contained in a system. They came up with a term named 'entropy' which could be quantified if the system a liquid, gas or solid consisting of particles, whose motions determine its state was at thermodynamic equilibrium. Thermodynamic equilibrium of a system is said to be achieved when the system is in not only in thermal but also in mechanical, chemical as well as radioactive equilibrium. Applications of thermodynamics describes how systems respond to various changes in their surroundings. This can be applied to a wide variety of topics in science and engineering like engines, chemical reactions, phase transitions and even black holes. What is Thermal Equilibrium? When two substances having different temperatures are introduced or kept together, heat energy flows from a substance at higher temperature to a substance at lower temperature. Also, heat continues to be transferred till their temperatures are equalized.

When this stage is achieved the substances are said to be in thermal equilibrium. Thus, we can generalize that 'heat energy always flows from a hotter body to a colder body till their temperatures are equalized'. Or to put it differently - 'A cold body does not become hot on its own, to raise its temperature, external heat energy must be supplied to it'.

We can also say, 'the temperature of a substance determines the direction of heat flow between the substances, when they are introduced together'.

Calorimetry Problems, Thermochemistry Practice, Specific Heat Capacity, Enthalpy Fusion, Chemistry

So, equilibrium occurs when observable or macroscopic changes in a system cease to change with the passage of time. Thermal equilibrium of a system does not mean complete uniformity or stability within a system.

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• An Explanation of Thermal Equilibrium and its Formulas With Examples

For example, a river system can be in thermal equilibrium when the macroscopic or externally measurable temperature is stable and not changing in time, even though the surrounding or spatial temperature distribution reflects degradation of water quality leading to changes in temperature.

Another example is when the thermometer is placed in contact with the patient's body, If the body temperature of the patient and that of the mercury in the clinical thermometer have reached thermal equilibrium, then the temperature of the thermometer is the same as the body temperature, hence the reading of the thermometer shows the body temperature of the patient.

Further illustration of this point is observed when food is put in the refrigerator, the heat from the food is transferred into the air of the refrigerator. Heat Two bodies brought in thermal contact will change their temperature until they are at the same temperature. Suppose we have a system of interest at temperature TS surrounded by an environment with temperature TE.

## Heat and temperature

Heat, presented by the symbol Q and unit Joule, is chosen to be positive when heat flows into the system, and negative if heat flows out of the system see Figure Heat is not the only way in which energy can be transferred between a system and its environment. The unit of work is the Joule. Another commonly used unit is the calorie.

The calorie is defined as the amount of heat that would raise the temperature of 1 g of water from The Joule and the calorie are related as follows: Heat Capacity When heat is added to an object, its temperature increases.

The heat capacity of an object depends on its mass and the type of material of which it is made. The heat capacity of an object is proportional to its mass, and the heat capacity per unit mass, c, is commonly used. In that case where m is the mass of the object. In order to determine the heat capacity of a substance we not only need to know how much heat is added, but also the conditions under which the heat transfer took place. For gases, adding heat under constant pressure and under constant temperature will lead to very different values of the specific heat capacity. Heat of Transformation When heat is added to a solid or a liquid, the temperature of the sample does not necessarily rise.

During a phase change melting, boiling heat is added to the sample without an increase in temperature.

### HEAT AND THE FIRST LAW OF THERMODYNAMICS

This heat must be supplied by the steam. Suppose the mass of the steam is m. The total heat required is Work Suppose a system starts from an initial state described by a pressure pi, a volume Vi, and a temperature Ti.

The final state of the system is described by a pressure pf, a volume Vf, and a temperature Tf. The transformation from the initial state to the final state can be achieved in a variety of ways see for example Figure If the pressure of a gas increases it can move a piston this happens in an engine.

On the other hand, if we increase the weight of the piston, work will be done on the system as the piston falls. If the piston is displaced by a distance ds, the amount of work done can be calculated as follows: Two possible ways to get from the initial state to the final state. The total work done during a finite displacement of the piston is now easy to calculate If W is positive, work was done by the system for example, the expanding gas lifts the piston. A negative value of W tells you that work was done on the system the piston is pressed down in order to compress the gas.

The amount of work done is equal to the area under the curve in the pV diagrams shown in Figure Clearly, the amount of work done depends on the path chosen. The work W for the path shown in Figure The work done for the paths shown in Figure The work done to move from pf, Vi to pf, Vf is calculated easily Clearly, W2b is always less then W2a, and we can make the amount of work done as small or as large as we want.

For example no work would be done if the transition follows the following path: