# Structural Biochemistry/Heat capacity

## Introduction

Heat is the energy transfer in body. The smaller the temperature change, the greater its capacity gets. The equation of heat capacity is as follow: ${\displaystyle C=dQ/dT}$

The heat capacity of an object is the amount of energy needed to raise the temperature of a substance 1 degree. The units are J/oC. Heat capacity is an extensive property. This means that a larger object has a larger heat capacity than a smaller object made from the same material. Heat Capacity = heat supplied / temperature rise The heat capacity of an object depends on both the quantity as well as the types of matter in the object. In order to compare heat capacties of different substances, we must relate heat capacity to the amount of material. One way to do this is to refer to a mole of substance. Then, the heat capacity will become the molar heat capacity. A more useful procedure is to compare heat capacities for one gram of material. This is called the specific heat capacity or simply specific heat. Specific heat is the quantity of heat required to increase the temperature of one gram of material one degree Celsius (or one kelvin). When divide the heat capacity of a material by its mass, we will have a specific heat. Specific heat = heat capacity / mass = C / m

To find the heat q required to raise the temperature of a sample by a certain amount, we multiply the specific heat of the substance, s, by the mass in grams, m, and the change in temperature,t. q = s x m x t

Furthermore, the heat capacity is given by the derivative of the internal energy with respect to temperature for a given energetic degree of freedom. There are many types of heat capacities: translational heat capacity, rotational heat capacity, vibrational heat capacity, and electronic heat capacity. [Physical Chemistry]. In the translational heat capacity, the translational energy-level spacing are extremely small. This makes the high temperature approximation is valid. In the rotational heat capacity, at the lowest temperaturs, there is insufficient thermal energy to provide for population of excited rotational energy levels. In contrast, as the heat capacity increases until the high temperature limit is reached. In the vibrational heat capacity, the high temperature limit is not applied to the vibrational degrees of freedom. The last heat capacity is the electronic heat capacity. In this heat capacity, there is no contribution to that constant volume heat capacity from the degrees of freedom since the partition function for the energetic degree of freedom is equal to the ground-state degeneracy. Also, the average energy is zero as well.

## Heat Capacity at Constant Volume

${\displaystyle C_{V}=(dU/dT)_{V}}$

It is usually called molar or specific heat capacity. U is the molar or specific internal energy, and T is the temperature. ${\displaystyle U,C_{V},}$ and ${\displaystyle T}$ are all state function.

It also can be written:

${\displaystyle dU=C_{V}dT}$

During this process, the volume should always be constant. If the volume changes during the process, even the initial value and final value are the same; it is not a constant volume. However, because ${\displaystyle U,C_{V}}$, and${\displaystyle T}$ are all state function, the equation applies to any process for initial and final values are the same.

## Heat Capacity at Constant Pressure

${\displaystyle C_{P}=(dH/dT)_{P}}$

${\displaystyle C_{P}}$ is molar and specific heat capacities. H is the molar or specific enthalpy, and T is the temperature. This process is a closed system process.

It also can be written:

${\displaystyle dH=C_{P}dT}$

The equation applies to any process for initial and values are the same, which means the pressure would not necessary be constant during the whole process because H, ${\displaystyle C_{P}}$, and T are all state function.

## Importance of Heat Capacity

The heat capacity, otherwise known as the specific heat, of various molecules is extremely important for many different reasons. It is because of the specific heat of the water molecule that allows for life to exist on planet earth. For example, because of water's unique specific heat of 1 cal to 1 gram of water, a large body of water , like a lake, can absorb and store a huge amount of heat from the sun in the daytime and during summer while warming up only a few degrees due to allocation, diffusion and spreading of heat throughout the water system. This coupled with waters high specific heat only changes the overall temperature by such a small amount. During nights and winter season, the gradually cooling water can warm the air. This is the reason that contributes to coastal areas having milder climates than inland regions. The high specific heat of water also tends to stabilize ocean temperatures, creating a favorable environment for marine life. Thus because of its high specific heat, the water that covers most of Earth keeps temperature fluctuations on land and in water within limits that permit life. Also, because organisms are primarily made of water, they are more able to resist changes in their own temperature than if they were made of a liquid with a lower specific heat.

## Reference

Engel, Thomas and Reid, Philip. Physical Chemistry. Pearson Education. Inc. 2006. Third Edition.

Smith, J. M., and Ness H. C. Van. Introduction to Chemical Engineering Thermodynamics. New York: McGraw-Hill, 1987. Print.