Heat, Internal Energy and Work

Have ever wondered how does a heat engine work? or what’s going in a glass of water kept on the table? When we normally observe a steady glass of water no kinetic or mechanical energy is noticed. But, when noticed under a microscope rapid motion of molecules is observed which determines the internal energy. Thermodynamics is the field of science that studies the combined effects of heat and work on changes in state. These changes and consequences are governed by specific rules, known as thermodynamic laws.

The heat energy generated or absorbed in various chemical processes transforms into various useable forms according to thermodynamic principles. We know that we can neither generate nor destroy energy. We can only transform it from one form to another. This principle is the foundation of energy transformation, and its use in many sectors is a significant application of thermodynamic terminology. Chemical reactions are also associated with variable quantities of energy. The study of the transfer of energy from one form to another is what thermodynamics is all about. It also investigates the relationship between heat and temperature, as well as energy and labor did.

What is Thermodynamics?

Thermodynamics is the concept related to the relation between energy and the work of a given system. The term thermodynamics was coined by William Thomas (Lord Kelvin)  in 1749. It is derived from Greek words ‘Thermes’ and ‘dynamis’ which means heat and energy or power respectively. Thermodynamics has a long history, it turns out that the approach to thermodynamics has had success in guiding the engineering of devices. They used the concept to convert thermal energy into mechanical energy for carrying out different works.

Thermodynamics can be defined as the branch of physics which deals with the relation of heat, work, and energy.

Thermodynamics is macroscopic science. conceptually, it is about converting the amount of thermal energy generated by the movement of particles into mechanical energy. But it is also to be noted that thermodynamics depends on the initial and final state of the system as it deals with the bulk system but not at the energy transformation or molecular constituent of the body.

For example, the steam engines used in train uses the force or energy produced by the steam to push the piston back and froth which at the same time is converted into rotational force by the wheels connected to the piston.  

The rules of thermodynamics are concerned with energy changes that occur during a process. They have nothing to do with the rate at which the reaction is taking place. In thermodynamic terminology, we frequently utilize generic words such as work, heat, and internal energy. Let us now learn a lot about these words and make sure we grasp them well.

Internal Energy

The energy stored inside the system is a result of the random movements of the particles, as well as the potential energies of the molecules as a result of their orientation, such energy is called Internal Energy.

Internal energy is defined as the total kinetic energy (due to random particle motion) and potential energy (related to particle state) present inside the system. Internal energy is affected by temperature, starting and ending states, but not by the journey. The internal energy of an ideal gas is determined solely by temperature, but the internal energy of a real gas is determined by both temperature and volume. 

• The unit of measurement for internal energy is Joule (J). 
• It is represented by the letter U. 

Internal Energy Formula

The Formula for Internal Energy is stated as,

ΔU = Q + W

where,

• ΔU is the internal energy of the system,
• Q is the heat supplied to the system, and
• W is work done by the system.

Relation between Enthalpy and Internal Energy 

The reason for the relationship between internal energy and enthalpy for an ideal gas is given here, as well as a mathematical technique to prove that the internal energy of an ideal gas is solely a function of temperature.

The internal energy (U) of an ideal gas is given as:

U = U(T)

However, the term enthalpy (H) is stated as:

H = U + PV                                                                                                                                                                                                  ……(1)

where, 

• P is the pressure, and 
• V is the volume of an ideal gas.

Now, let’s apply the ideal gas equation in the above equation, which is given by:

PV = RT

where, 

• R is the ideal gas constant, and
• T is the temperature of an ideal gas.

⇒ H = U + RT

Also, the Enthalpy of an ideal gas is given as:

H = H(T)

Since, the specific heat at constant volume and pressure (C_v and C_p) which are temperature-dependent are given by:

dU = C_v (T) dT

dH = C_p (T) dT

Using the above equations, specific heat ratio k is given as:

k = C_p / C_v=U / H

For an ideal gas, this is the relationship between internal energy and enthalpy.

HEAT

Heat is defined in thermodynamics as energy in motion. It is the energy that the kinetic energy of the substance’s molecules held. Heat and thermodynamics are crucial in assisting process designers and engineers in optimising their operations.

It also enables them to economically capture the energy involved with chemical processes. Heat moves from higher to lower temperatures. This notion aids scientists in the development of different heat engines. When temperature disparities occur, heat is the energy in transit. Internal energy is equal to the sum of internal kinetic energy and internal potential energy caused by molecular attraction forces. A heated body has more internal energy than a cold one of the same size.

The heat entering the system is considered positive (+ve). While the heat leaving the is considered as negative (-ve).

The factors that affect the amount of heat flow are:

• The mass of the substance (m).
• The temperature difference between the two objects (ΔT).
• And at last the nature of the substance.

This implies that,

Q ∝ mΔT

or 

Q = cmΔT

where c is the proportionality constant (called specific heat capacity). It is determined by the body’s nature.

Work

Work done by a system, according to thermodynamics, is the total amount of energy that the system and its surroundings exchange within itself. The quantity of work done is determined by external elements in the environment. 

These variables might include an external force, variations in temperature, pressure, or volume, and so on. Thermodynamics also relates to another term ‘work’ which is concerned with the transfer of energy. Work is done by the gas during expansion and work is done on the gas during compression. The work depends upon both path and initial and final state.

The work done by the system is positive (+ve) and work done on the system is negative (-ve). For example, let’s assume a piston contains gas. When the piston moves upwards due to the expansion of gas the work is said to be done by the gas and is positive. whereas, if the piston moves inward the work is said to be done on the gas and is negative.

Fig. Work done by the gas on a piston.

The formula of work done is given by,

W = ∫P.dV

Sample Problems

Problem 1.When a piece of ice is placed on your hand, you get a cold sensation, why?

Solution.

When a piece of ice is placed on hand a cold sensation is felt because the temperature of ice is less than that of the hand. Hence, the heat gets transferred from the hotter body to colder i.e. from the hand to ice.

Problem 2. Can the absolute value of internal energy be determined? Why or why not?

Solution. 

No, the absolute value of internal energy cannot be determined because it is the sum of different forms of energies and some of which cannot be determined actually.

Problem 3. What are the factors that affect the internal energy of a system?

Solution. 

Temperature and volume can be responsible for the alteration of internal energy as the temperature of the system increase molecules start to move fast and hence, the kinetic energy also increases simultaneously. 

Problem 4. A cylinder with a movable piston consists of gas on which a heavy block is placed. Suppose the total mass of the block and the movable piston is 51 kg. When 1070 J  of heat flows into the gas, the internal energy of the gas increases by 790 J. What would be the distance of piston rise?

Solution.

Given that, 

Total heat supplied = work done + change in internal energy

Now,

Work done = 1070 – 790 = 280 J

Let’s consider s be the distance moved by piston,

The workdone is given by 

W = F.s

s = 280 / F

s = 280/ 51×10

s = 0.54 m

Problem 5. An electric heater is supplying heat to a system at a rate of  50. If the system performs work of 25  Joules per second. At what rate is the internal energy increasing?

Solution.

Given, 

Heat supplied to the system (Q) = 50 W

Work done performed (W) = 25 J/s

As per the equation,

Q = U + W

U = 50 -25

   = 25 J/s

Therefore, the internal energy of the system increases by the rate of 25 J/s.

Problem 6. What is considered to be the foundation of Thermodynamics?

Solution. 

The law of conservation of energy that “energy can neither be created nor be destroyed” and transfer of heat from a hot body to a cold body is the foundation of Thermodynamics.