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First Law of Thermodynamics

  • Last Updated : 05 Jul, 2021

Thermodynamic rules are straightforward to state. Do you aware that thermodynamics principles apply to the human body? When we’re in a room full of people, we start to sweat and feel heated, and if a room is tiny, the perspiration becomes excessive. This occurs because your body is attempting to cool itself, and heat is transferred from the body through perspiration. This necessitates the application of the first law of thermodynamics.

We must first comprehend a relationship between work and heat, as well as an idea of internal energy, before moving on to the first law of thermodynamics. Energy, like matter, is always conserved, meaning it cannot be generated or destroyed but may be converted into different forms. A thermodynamic property cites the energy which is related to the system’s molecules, including potential and kinetic energy is called the internal energy of a system.

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When a system changes as a result of the relation of work, heat, and internal energy, multiple energy transfers and conversions occur. However, the net change in total energy throughout these exchanges is zero. In the same way, the first law of thermodynamics explains that heat is a type of energy. It means that the principle of energy conservation governs thermodynamic processes. The Law of Conservation of Energy is another name for the fundamental law of thermodynamics.

What is the First Law of Thermodynamics?

The first law of thermodynamics states that the total energy of an isolated system is constant. Energy can be transformed from one form to another, but can neither be created nor destroyed.

The first law of thermodynamics.

Internal energy is a state variable in a thermodynamic system that is in equilibrium. The internal energy difference between the two systems is equal to heat transfer into the system minus work done by the system.

According to the first rule of thermodynamics, the universe’s energy does not change. It can be transferred between the system and the surroundings, but it cannot be produced or destroyed. The law is primarily concerned with energy states as a result of work and heat transmission. It reinterprets the notion of energy conservation.

We may use the popular example of a heat engine to help you grasp the meaning of the First Law. Thermal energy is transformed into mechanical energy in a Heat engine, and the process is also reversed. The majority of heat engines are classified as open systems. A heat engine’s primary working concept is to take advantage of the many interactions between heat, pressure, and volume of a working fluid, which is generally a gas. It’s not uncommon for gas to turn into a liquid and then back to a gas.

First Law of Thermodynamics Equation

According to this rule, some heat supplied to the system is utilized to modify the internal energy, while the remaining is utilized by the system to perform work. Mathematically,

ΔQ = ΔU + ΔW


  • ΔU is the change in internal energy of the system,
  • ΔW is the work done by the system, &
  • ΔQ is the heat supplied to the system.

There is a net heat transfer into the system if Q is positive, and there is work done by the system if W is positive. As a result, positive Q provides energy to the system whereas positive W depletes it. When heat is applied to a system, internal energy tends to rise, and vice versa.

Things to Remember

  • The internal energy of an ideal gas is only a function of temperature.
  • Internal Energy is a system’s point function and attribute. Internal energy is a broad (mass-dependent) characteristic, whereas specific energy is a narrow (mass-independent) attribute (independent of mass).
  • Energy (E) is always constant in an isolated system.

Limitations of First Law

  1. The first law of thermodynamics has a limitation in that it states nothing about the direction of heat flow.
  2. It is not feasible to reverse the procedure. In actuality, the heat does not entirely convert to labor. We could move ships across the ocean by extracting heat from the ocean’s water if it had been feasible to turn all of the heat into work.
  3. It makes no distinction between whether the process is spontaneous or not.

Perpetual Motion Machine of First Kind (PMM1)

It is impossible to build a machine that can do mechanical work indefinitely without spending any energy. The perpetual motion machine of the first type is a hypothetical device like this. These machines contradict the first rule of thermodynamics and do not exist in the actual world.

Thermodynamic Cycles

  • The overall energy in an isolated system remains constant. The net heat provided to the system equals the net work done by the system in a thermodynamic cycle. The batteries we use, for example, transform chemical energy into electrical energy. Electric bulbs convert electrical energy into light energy as well.
  • The work done on, or by, a gas is determined not only by the gas’s initial and final states, but also by the process, or path, that leads to the final state. The quantity of heat transported into or out of a gas is also determined by the beginning and final states, as well as the process that creates the final state.
  • Internal energy is the same as the potential energy of an item at a certain height above the earth or the kinetic energy of a moving object. The internal energy of a thermodynamic system transforms to either kinetic or potential energy in the same manner that potential energy changes to kinetic energy while preserving the system’s overall energy. Internal energy may be stored in the system in the same way as potential energy can. The first rule of thermodynamics allows for a wide range of potential system states, yet only a few are seen in nature.

First Law of Thermodynamics for a Closed System

The product of the pressure applied and the change in volume that happens as a result of the applied pressure is the work done for a closed system:

W = – P ΔV


  • P denotes the system’s constant external pressure, and
  • V denotes the volume change.

This is referred to as Pressure-Volume work.

The internal energy of a system rises or falls in response to work interactions that occur across its limits. When work is done on the system, the internal energy increases, but it decreases when work is done by the system. Any heat exchange between the system and its surroundings alters the system’s internal energy. However, the total change in internal energy is always zero since energy remains constant (according to the first rule of thermodynamics). If the system loses energy, it is absorbed by the surroundings. If energy is absorbed into a system, the energy must have been released by the environment:

ΔUsystem = −ΔUsurroundings


  • ΔUsystem is the change in the total internal energy of the system, and
  • ΔUsurroundings is the change in the total energy of the surrounding.

There are four processes involved in the closed system:

  • Isothermal Process: A process in which temperature is constant. Internal heat energy is always zero for this process.
  • Adiabatic Process: A process in which heat neither leaves nor enters the system. Heat transfer is always zero for this process.
  • Isobaric Process: A process in which external pressure is always constant.
  • Isochoric Process: A process in which volume is always constant. The work done is always zero for this process.

Sample Problems

Problem 1: Find out the internal energy of a system that has constant volume and the heat around the system is increased by 30 J?


Given that, 

Heat Transfer, ΔQ = 30 J

For constant volume, ΔV = 0

W = P ΔV

    = 0

The formula for internal energy is given as:

ΔU = ΔQ – W

      = 30 J – 0

      = 30 J

Hence, the change in internal energy of the system is 30 J.

Problem 2: Calculate the change in the internal energy of the system if 2000 J of heat is added to a system and a work of 1500 J is done.



Heat added to a system, ΔQ = 2000 J

Work done on the system, W = 1500 J

The formula for internal energy is given as:

ΔU = ΔQ – W

     = 2000 J – 1500 J

    = 500 J

Hence, the change in internal energy of the system is 500 J.

Problem 3: What is the significance of the first law of thermodynamics to the environment?


Energy cannot be generated or destroyed, according to the first law; it can only be changed from one form to another. All living species on Earth rely on the sun for their energy. Photosynthesis is the process through which plants transform solar energy into chemical energy. These energies are not returned to the solar system by the plants; instead, they are passed on to herbivores that eat green vegetation. Carnivores use some energy gained by herbivores, while some energy obtained by herbivores is passed to decomposers when the herbivores die.

Problem 4: State First Law of Thermodynamics.


The First Law of Thermodynamics states that heat is a form of energy, and thermodynamic processes are therefore subject to the principle of conservation of energy. This means that heat energy cannot be created or destroyed. It can, however, be transferred from one location to another and converted to and from other forms of energy.

Problem 5: A gas in a closed container is heated with 20J of energy, causing the lid of the container to rise 3 m with 4 N of force. What is the total change in energy of the system?



Heat supplied to the container, ΔQ = 20 J

Rise in lid of the container, Δx = 3 m

Force applied on the container, F = 4 N

We are not given a value for work, but we can solve for it using the force and distance. Work is the product of force and displacement.

W = F Δx

   = 4 N × 3 m

   = 12 J

The formula for internal energy is given as:

ΔU = ΔQ – W

      = 20 J – 12 J

      = 8 J

Hence, the change in internal energy of the system is 8 J.

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