How Do Heat, Internal Energy, and Work Interact in Thermodynamics?
Introduction to Heat
We are quite familiar with the term heat that can be described as feeling too hot or too cold.
We know that the sun is the main source of the earth’s heat.
Only a fraction of the sun’s heat reaches the earth which is sufficient for life to exist on earth.
What happens if the intensity of sun rays reaching the earth increases?
We would start feeling hot and prefer to stay at home and sit under the AC.
Now, the question arises why we feel hot outside and cold under the AC?
So, the chill we feel is because of the flow of heat.
What is Internal Energy?
We know that temperature is the measure of the molecular kinetic energy of the particles in a system.
This kinetic energy is distributed amongst the translational motion, rotational motion, and vibrational motion of a molecule.
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There is also molecular potential energy by the electromagnetic force acting upon the atoms of an individual molecule and between each separate molecule.
The sum of all these energies exhibited by the particles of a system is called the internal energy of the system denoted by the letter U.
This energy is associated with atomic motion and is directly proportional to the temperature of the system.
So, higher is the temperature, higher is the internal energy, and vice versa.
What is Internal Energy of a System?
The internal energy of a system can be increased by increasing the heat transfer, but because of factors such as surface deformation, friction, there may be some energy loss.
We learned that for a particular system, there will always be a conservation of energy.
Let’s say, a stone is falling freely under gravity, it possesses both potential energy and kinetic energy.
So, let’s add internal energy of the objects to this list, and restate conservation of energy with the equation below:
ΔPE +ΔKE +ΔU = 0
Here, ΔPE = change in potential energy
ΔKE = change in kinetic energy, and
ΔU = change in internal energy
So, if any of these quantities change, then some energy is transformed from one form to another.
Internal Energy Formula
Consider an ideal gas:
Its total energy = Internal energy because of the kinetic energy of molecules.
Its potential energy is zero because there is no attraction between the molecules.
So, TE = 0 + KE
Using the First Law of Thermodynamics
Consider a thermodynamic system having an ideal gas packed under the piston:
On adding Q amount of heat to this system, several factors of gas increments:
Molecular speed
Heat and temperature
Pressure
The piston moves upward; it means some work is done by this thermodynamic system to bring the piston up.
Here, this thermodynamic system absorbs heat. It retains a part of heat with itself and uses another part by working in raising the piston.
The part of heat absorbed by the system increases its internal energy.
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The internal energy was U1 after piston rise; the internal energy is U2 and U2 > U1.
So, the change in internal energy is:
ΔU = U2 - U1
Here, ΔU is the heat retained by the system, and
W = The work done by the system to raise the piston.
So, Q (Amount of heat provided) = ΔU + W
Why the system kept ΔU instead of U2?
Because the heat absorbed by this system got converted to the work done in raising the piston and only a difference of the energy got by the system.
This is how we got the formula, Q = ΔU + W.
In differential form:
მQ = მU + მW…..(1)
Relation Between Enthalpy and Internal Energy
We define enthalpy as the heat content of a system at constant pressure.
We know that: H = U + PV
This relationship says:
Heat content in the system is equivalent to the internal energy of molecules or atoms (PE + KE) at quantum level + PV (the work done to establish the system at external pressure P and volume V from space.
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So, work done can be seen in this diagram.
The unit of enthalpy is KJ/mol.
In thermodynamics, H has no significance; let’s understand why?
If we go at the microscopic level to estimate the amount of energy each molecule possesses, it becomes an impossible task to do so.
Like we can’t measure the quality of a person like singing but can compare by the number of awards you won (Quantifying). Similarly, we can’t measure the energy absorbed by the system.
Therefore, to consider H as an enthalpy, it becomes a matter of confusion.
So, that’s why we study ΔH in place of H.
So, ΔH and ΔU instead of H and U.
Since the volume expanded from V1 to V2
At constant pressure equation becomes:
ΔH = U + P (V2 - V1)
ΔH = U + PΔV
At constant volume: ΔH = U + VΔP…(2)
FAQs on Heat, Internal Energy, and Work: A Complete Physics Guide
1. What is the main difference between heat and work in thermodynamics?
In thermodynamics, both heat and work are methods of energy transfer, but they differ fundamentally. Heat (Q) is the transfer of energy due to a temperature difference between a system and its surroundings, involving the random motion of molecules. In contrast, work (W) is the transfer of energy through an ordered, macroscopic force acting over a distance, such as the expansion of a gas pushing a piston.
2. What is internal energy, and can you provide a real-world example?
Internal energy (U) represents the total energy contained within a thermodynamic system. It is the sum of the kinetic energies (from the motion of molecules) and potential energies (from the intermolecular forces) of all the particles in the system. A simple example is heating a pot of water. As you supply heat, the water molecules move faster, increasing their kinetic energy and thus the water's internal energy, which we observe as a rise in temperature.
3. How are heat, work, and internal energy connected by the First Law of Thermodynamics?
The First Law of Thermodynamics provides the connection between these three concepts. It is a statement of energy conservation, expressed as: ΔU = Q - W. This equation means that the change in a system's internal energy (ΔU) is equal to the heat added to the system (Q) minus the work done by the system (W). A system's energy can be increased by heating it or by doing work on it.
4. Why are the sign conventions for heat and work important in physics?
Consistent sign conventions are crucial for correctly applying the First Law of Thermodynamics. In physics, the standard convention is as follows:
Heat (Q) is positive when it is added to the system.
Work (W) is positive when it is done by the system on its surroundings (e.g., expansion).
Understanding this helps determine whether the system's internal energy will increase or decrease during a process.
5. Under what condition does the change in internal energy (ΔU) equal the heat transferred (Q)?
The change in internal energy (ΔU) is equal to the heat transferred (Q) when no work is done by or on the system (W = 0). This occurs in a process where the volume is held constant, known as an isochoric process. Since work done by a gas is given by W = PΔV, if the volume change (ΔV) is zero, then work (W) is zero, and the First Law simplifies from ΔU = Q - W to ΔU = Q.
6. How can a system's internal energy increase without a change in its temperature?
A system's internal energy can increase without a temperature change during a phase transition. For example, when ice at 0°C melts into water at 0°C, heat energy (known as latent heat) is absorbed. This energy does not increase the kinetic energy of the molecules (so the temperature remains constant) but is used to break the bonds of the ice's crystal structure, thereby increasing the system's potential energy and, consequently, its total internal energy.
7. What is the difference between a state function and a path function in this context?
The difference lies in whether the value depends on the journey or just the destination.
A state function depends only on the initial and final states of the system, not the path taken. Internal energy (U) is a state function.
A path function is a quantity whose value depends on the specific path taken between the initial and final states. Both heat (Q) and work (W) are path functions.
8. In which thermodynamic process is the change in enthalpy (ΔH) equal to the heat supplied (Q)?
The change in enthalpy (ΔH) is equal to the heat supplied (Q) during a process that occurs at constant pressure, known as an isobaric process. Enthalpy (H) is defined as H = U + PV. For a constant pressure process, the first law (ΔU = Q - PΔV) can be rearranged to show that the heat supplied is Q = ΔU + PΔV. This expression is exactly equal to the change in enthalpy, so for an isobaric process, ΔH = Q.
9. What is an adiabatic process, and how does it affect the internal energy of a system?
An adiabatic process is one where no heat is transferred between the system and its surroundings (Q = 0). In this case, the First Law of Thermodynamics becomes ΔU = -W. This means any work done by the system (like a gas expanding) comes directly from its internal energy, causing its temperature to decrease. Conversely, if work is done on the system (compression), its internal energy and temperature will increase.
