A system’s internal energy is defined as the sum of the random internal kinetic energies of the atoms and the total internal potential energies due to the bonds between atoms.
A simple example is a battery, which uses internal energy to produce chemical reactions.
Furthermore, the internal energy is a state function, not a path function. When a system transitions from one state to another, the change in internal energy is determined by the initial and final states, not by the process used to make the transition.
Internal energy is represented by the symbol U, and its unit is the Joule. Internal energy is typically calculated per mole of a substance. The change in internal energy U is usually calculated for most practical purposes.
Table of Contents
Internal Energy of a System
To get the internal energy when a system goes from its initial state to its final state, we use the following equation.
ΔU = Ufinal – Uinitial
Where
Ufinal : Internal energy of the final state
Uinitial : Internal energy of the initial state
In a closed cycle, the system comes back to its initial state. As a result, the internal energy change for a closed cycle is zero.
Real life Examples of Internal Energy
There are many real-life examples of internal energy of a system, some of which are:
- Boiling Water: When water is heated on a stove, the heat energy causes the molecules in the water to move faster and collide more frequently. This increased kinetic energy of the water molecules results in an increase in the internal energy of the system.
- Car Engine: When fuel is burned in the engine of a car, the heat energy released causes the temperature of the gas to increase, resulting in an increase in the internal energy of the gas.
- Solar Heating: When sunlight falls on a surface, the energy is absorbed by the material, increasing the internal energy of the system. This can be observed in solar heating systems, where the absorbed energy is used to heat water for household use.
- Fire: When wood or any other fuel is burned, the heat energy released causes the temperature of the surrounding air to increase, resulting in an increase in the internal energy of the system.
- Refrigeration: In a refrigeration system, the compressor increases the pressure and temperature of the refrigerant, which increases its internal energy. This energy is then transferred to the outside environment through the condenser, resulting in cooling inside the refrigerated space.
Overall, internal energy is a fundamental concept in thermodynamics and can be observed in many different systems and processes in our daily lives.
Internal Energy- Key Points
- The internal energy depends only upon the quantity of the substance contained in the system. Hence, it is an extensive property.
- The internal energy of ideal gases is solely determined by temperature. As a result, because the temperature remains constant in isothermal processes, there is no change in the internal energy of an ideal gas, i.e., ΔU=0. This is due to the fact that the intermolecular forces of attraction between molecules in an ideal gas are negligible. When the ideal gas expands, no work is done to overcome the intermolecular forces. As a result, at a constant temperature, its internal energy remains constant.
- Total internal energy measurement is not possible. Its variation is measured and expressed by ΔU.
Internal Energy of Ideal Gases
The ideal gas is a gas of point objects that interact only through elastic collisions. In this case, the kinetic energy is made up of the translational energy of the individual atoms.
As a result, changes in internal energy in an ideal gas are only caused by changes in kinetic energy. The energy in this case is solely determined by its pressure, volume, and thermodynamic temperature. The value is proportional to its mass (number of moles), temperature, and specific heat at the constant volume of the gas.
Internal energy and Specific Heat
The relationship between specific heat and internal energy is important in thermodynamics and can be used to understand the behavior of substances as they undergo changes in temperature and pressure.
The relationship between specific heat and internal energy is given by the equation:
Q = mCΔT
where:
Q is the heat added to the system;
m is the mass of the substance being heated;
C is the specific heat of the substance;
ΔT is the change in temperature.
- When a substance is heated, its internal energy increases, and this leads to an increase in temperature. The amount of heat required to raise the temperature of a substance depends on its specific heat and the amount of substance being heated.
- The specific heat of a substance depends on its molecular structure and the way in which its particles interact with one another. The internal energy of a system depends on its temperature, pressure, and the number of particles it contains.
Internal energy and enthalpy
Relation between Internal Energy and Enthalpy of a System:
| Internal Energy (U) | Enthalpy (H) |
|---|---|
| 1. It is the sum of all forms of energy in a system, including kinetic and potential energy. | 1. It is the sum of internal energy and the product of pressure and volume of a system. |
| 2. It is a state function that depends only on the current state of the system and not on the path taken to reach that state. For example, Example 2: If a gas is compressed from 1 atm to 10 atm, and then allowed to expand back to 1 atm, the internal energy c | 2. It is also a state function that depends only on the current state of the system and not on the path taken to reach that state. For example, If a system undergoes a process where no work is done against external pressure, such as an isochoric (constant volume) process, then the change in enthalpy will be equal to the heat transferred into or out of the system. |
| 3. It is denoted by the symbol U. | 3. It is denoted by the symbol H. |
| 4. Change in internal energy (ΔU) is equal to the heat transferred (q) plus the work done (w) on or by the system, i.e., ΔU = q + w. For example, Example 8: If a system absorbs 500 J of heat and does 100 J of work on its surroundings at constant volume, then the change in internal energy will be ΔU = q + w = 500 J + 100 J = 600 J. | 4. Change in enthalpy (ΔH) is equal to the heat transferred (q) at constant pressure, i.e., ΔH = q_p. |
| 5. It is related to temperature and the number of particles in the system. | 5. It is related to temperature, pressure, and the number of particles in the system. |
| 6. The internal energy of a gas depends on its temperature and the number of gas molecules in the system. | 6. The internal energy of a system does not take into account any work done against external pressure, i.e., it does not account for changes in volume. |
| 7. Internal energy can be calculated using the first law of thermodynamics, which is based on the principle of conservation of energy. For instance, If a system is adiabatic (no heat transfer) and does no work on its surroundings, then the change in internal energy will be zero since no energy is transferred into or out of the system. | 7. Enthalpy can be calculated using the equation H = U + PV. |
Internal Energy and Entropy
Internal energy and entropy of a system are related in the following ways:
- Internal energy is a measure of the total energy in a system, including the kinetic and potential energy of its particles. Entropy, on the other hand, is a measure of the disorder or randomness of the system.
- The change in internal energy of a system can be related to the heat added to or removed from the system and the work done on or by the system, as given by the first law of thermodynamics: ΔU = q + w.
- The change in entropy of a system can be related to the heat transferred to or from the system and the temperature at which this transfer occurs, as given by the second law of thermodynamics: ΔS = q/T.
- The entropy of a system tends to increase with time, as energy is redistributed and the system moves toward a state of greater disorder.
- When a system undergoes a process in which it gains or loses heat, both the internal energy and entropy of the system can change. For example, if a gas is compressed and then allowed to expand, the internal energy of the gas may remain the same, but its entropy will increase due to the increased randomness of its particles.
- The relationship between internal energy and entropy can be used to determine whether a particular process is spontaneous or requires external energy input. If the entropy of a system increases during a process, it will tend to occur spontaneously, while a decrease in entropy will require external energy input to occur.
Overall, the relationship between internal energy and entropy highlights the fundamental role that energy and randomness play in the behavior of thermodynamic systems.
How is system internal energy related to temperature?
The internal energy of a system is related to its temperature through the kinetic energy of its particles. At a molecular level, the temperature of a system is a measure of the average kinetic energy of its particles. The internal energy of a system includes the kinetic and potential energy of all the particles within the system. Therefore, as the temperature of a system increases, the kinetic energy of its particles also increases, leading to an increase in the internal energy of the system.
This relationship between temperature and internal energy is described by the specific heat capacity of the material, which is the amount of energy required to raise the temperature of a unit mass of the material by one degree. The specific heat capacity is a measure of the ability of the material to store energy in the form of internal energy. Materials with a higher specific heat capacity require more energy to increase their temperature compared to materials with a lower specific heat capacity.
Overall, the relationship between system internal energy and temperature is a fundamental concept in thermodynamics and is essential for understanding the behavior of materials and systems in various real-world applications.
Some real-life examples that illustrate the relationship between system internal energy and temperature:
- Cooking: When we cook food, we apply heat to increase the temperature of the food. This increase in temperature leads to an increase in the internal energy of the food, which causes it to cook or change state.
- Heating and Cooling Buildings: Heating and cooling systems in buildings work by transferring heat to or from the air or water in the system. This transfer of heat results in an increase or decrease in the internal energy of the air or water, which affects the temperature of the building.
- Car Engines: Car engines work by burning fuel, which releases energy and increases the temperature of the gases inside the engine. This increase in temperature results in an increase in the internal energy of the gases, which is then converted into mechanical energy to power the car.
- Boiling Water: When we heat water on a stove, the temperature of the water increases, which increases the internal energy of the water molecules. Eventually, the internal energy becomes high enough to cause the water to boil and change state from a liquid to a gas.
- Refrigeration: Refrigeration systems work by removing heat from a space and transferring it to the outside environment. This results in a decrease in the internal energy of the air or water in the refrigerated space, which lowers the temperature of the space.
These examples illustrate how changes in temperature can lead to changes in the internal energy of a system and can be observed in many real-world applications.
Frequently Asked Questions
| # | Question | Answer |
|---|---|---|
| 1 | What is the definition of system internal energy? | The sum of the kinetic and potential energies of the particles that make up a system. |
| 2 | What is the first law of thermodynamics in terms of system internal energy? | The change in system internal energy is equal to the heat added to the system minus the work done by the system. |
| 3 | How is system internal energy related to temperature? | The internal energy of a system is directly proportional to its temperature. |
| 4 | How is system internal energy related to enthalpy? | Enthalpy is the sum of the internal energy of a system and the product of its pressure and volume. |
| 5 | How is system internal energy related to specific heat? | The specific heat is the amount of heat required to raise the temperature of one unit of mass of a substance by one degree Celsius. |
| 6 | What is the difference between system internal energy and enthalpy? | Enthalpy includes the energy required to do work against a constant external pressure, while internal energy does not. |
| 7 | How does the internal energy of a system change during a phase change? | The internal energy of a system remains constant during a phase change, as the energy is used to break or form intermolecular bonds. |
| 8 | What is the relationship between system internal energy and heat capacity? | Heat capacity is the amount of heat required to raise the temperature of a system by one degree Celsius, per unit mass or volume. |
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