Heat, Work, and Energy

Introduction

According to the first law of thermodynamics, energy can never be created nor destroyed; it can only be transferred from one system to another or converted to another form of energy. A chemical system can either absorb or evolve heat energy. The process in which heat is absorbed is termed the endothermic process, whereas the process in which heat is evolved is termed an exothermic process. Chemical reactions work with the use of heat. For example, when a rocket burns the fuel, it lifts off the space shuttle from the ground. In this case, the rocket is doing the work by applying a force, and also, when a space shuttle lifts off, it releases large amounts of heat and light. The first law of thermodynamics relates to the heat and work for a change in the system’s internal energy.

ΔEsys = Q + W

Here, both heat and work state the processes by which energy is transferred to or from a system.

Definition of Internal energy

Internal energy is one of the most important terms of thermodynamics. It is the sum of the kinetic energy and the potential energy of the particles of a system. It is represented by ‘E’ or ‘U’. The internal energy can be easily understood by the example of an ideal gas because the particles in ideal gas have no potential energy and do not interact with each other. So in the case of an ideal gas, the internal energy is just the sum of kinetic energies of the particles in the gas. According to kinetic molecular theory, the temperature of a gas is directly proportional to the kinetic energy of the particles present in the system.

So the internal energy of the ideal gas is:

Esys = 3/2 RT

where R is the ideal gas constant (in Joules per mole kelvin or J/mol-K)

and T is the temperature (in kelvin or K)

For a complex system, internal energy can not be measured directly. However, the internal energy is proportional to the temperature. So, in a complex system, we monitor the change in internal energy of the system by observing the temperature change. We assume that whenever the temperature increases, the internal energy increases too. 

Internal Energy Formula

The energy stored in a system is because of the random motion of the particles and their potential energies due to their orientations. The energy that occurs due to random motions has many forms like translational energy, rotational energy, and vibrational energy. It is represented by ‘U’. So, we can say that, in all the processes, the internal energy from one state to another will remain the same.

In empirical form, it can be written as:

ΔU = Q – W

Here, ΔU = Total change in internal energy of a system; 

Q = Heat exchange that takes place between system and surroundings; and

W = Work done on the system or work done by the system

Enthalpy

Enthalpy (H) can be defined as the sum of internal energy (U) and the product of the volume and pressure (PV) of a system. Whenever a process takes place at constant pressure, the heat evolved is equal to the change in enthalpy (the heat may either be released or evolved from the system). In mathematical terms, the enthalpy is, H = U + PV.

Enthalpy is purely a state function, and it depends on the temperature, pressure, and volume. 

• The change in enthalpy for initial and final states of a process can be expressed as:

             ΔH = ΔU + ΔPV

• If both the temperature and pressure remains constant and the work is limited to pressure-volume work, then the change in enthalpy can be calculated with:

ΔH = ΔU + PΔV

• Also, when the pressure is constant, the heat flow (Q) for the process is equal to the change in enthalpy. It is defined by the equation:

ΔH = Q

By examining whether the reaction is exothermic or endothermic, we can find the relationship between ΔH and Q. If the reaction is exothermic, Q will be less than 0, and ΔH will also be negative. If the reaction is endothermic, Q will be greater than 0, and ΔH will also be positive.

Relation between Internal Energy and Enthalpy

The following equations explain the relationship between Internal energy ‘U’ and Enthalpy ‘H’ for an ideal gas.

For an ideal gas, the equation for internal energy is given by:

U = U(T); and 

Enthalpy is:

H = U + PV

Using the ideal gas equation, we can substitute PV = RT, so we get

H = U + RT

For the above equation, R is the universal gas constant.

So, the enthalpy of an ideal gas is:

H = H(T)

As we know, the specific heat at constant pressure and volume is temperature dependent so,

dU = Cv (T) dT; and

dH = Cp (T) dT

Using both the equations, the specific heat ratio is given as,

k = Cp/ Cv 

k = U/ H

Difference between enthalpy and internal energy:

The basic differences between the internal energy and enthalpy are:

• The term internal energy is used to define the total energy of a system, whereas enthalpy is the relationship between the surroundings and the system.
• The empirical formula for Internal energy is given as ΔU = Q + W, whereas the formula for Enthalpy is H = U + PV.

Conclusion:

Whenever the energy is transferred between thermodynamic systems by thermal interactions, the energy transfer is referred to as heat. Work is the energy transfer of any process other than heat. The two terms, work and heat, are interrelated to each other. Work can be completely converted into heat, but heat can never be converted into work. For a closed system, the change in internal energy ΔU is related to work W and heat Q.

ΔU = Q + W

It means that a system’s internal energy is affected by two parameters: heat and work.

At a constant volume, the heat absorbed is equal to the change in the system’s internal energy. When the pressure is constant, the heat absorbed is equal to the enthalpy of the system.