How Does Heat Capacity Affect Internal Energy in Physics?
Thermodynamics is a branch of physics that studies function, heat, and temperature, as well as their relationships with radiation, electricity, and matter's physical properties.
Thermodynamics is used in a broad range of scientific and engineering disciplines, including physical chemistry, biochemistry, chemical engineering, and mechanical engineering, as well as more complex areas including meteorology.
The theory of the relationship between heat, work, temperature, and energy is known as thermodynamics. Thermodynamics, in its broadest sense, is concerned with the transition of energy from one location to another and from one type to another. The three laws of thermodynamics govern the behaviour of these quantities, and provide a quantitative definition using observable macroscopic physical quantities but can be described by statistical mechanics in terms of microscopic constituents.
The first theorem of thermodynamics, also known as the law of energy conservation. The difference in a system’s internal energy is equal to the difference between heat added to the system from its surroundings and work done by the system on its surroundings.
The second law of thermodynamics describes how heat is transferred from one place to another. Heat does not naturally flow from a cooler to a hotter area, or, to put it another way, heat at a given temperature cannot be turned entirely into function.
The Third Law of Thermodynamics is one of the most important laws of thermodynamics.
If the temperature reaches absolute zero, the entropy of a perfect crystal of an atom in its most stable state tends to zero.
In this article, we will discuss the sub-topic of thermodynamic, heat capacity and internal energy.
Internal Energy of Thermodynamics
The energy found within a thermodynamic device is known as its internal energy.
It's the amount of energy used to construct or plan a structure in any given internal state. It excludes the kinetic energy of the system's motion as a whole, as well as the potential energy of the system as a whole due to external force fields, which includes the energy of movement of the system's surroundings. It maintains track of the system's energy benefits and losses as a result of changes in its internal environment. The difference between a reference zero specified by a normal state and the internal energy is determined.
Internal energy is a broad property that cannot be directly determined.
Transfers of matter or energy as heat, as well as thermodynamic function, are the thermodynamic processes that characterise internal energy. Changes in the system's several factors, such as entropy, volume, and chemical composition, are used to calculate these processes.
The internal energy formula is written as U = Q W in equation form.
The change in the internal energy formula U of the device is represented by ΔU. The number of all heat flow into and out of the system is Q, which is the net heat transmitted into the system. W denotes the system's network or the amount of all work performed on or by the system. The internal energy equation is used to calculate the change in the internal energy of a gas.
The internal energy equation in thermodynamics is also called the first law of thermodynamics equation is ΔU = Q − W.
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The internal energy of a closed thermodynamic system.
The differentials of each expression can be used to express this relationship in infinitesimal terms, but only the internal energy is an exact differential.
The change in internal energy for a closed system with only heat and work transfers is
δU = δQ - δW
The first law of thermodynamics is expressed in this way.
Other thermodynamic parameters should be used to express it. Each word is made up of an intensive variable (a generalised force) and an infinitesimal extensive variable that is conjugate to it (a generalised displacement).
The mechanical work performed by the machine, for example, can be connected to the pressure P and volume shift δV. The volume shift is the substantial generalised displacement, while the pressure is the intensive generalised force:
δW = PδV
This defines the direction of work W, to be energy transfer from the working device to the surroundings, indicated by a positive term.
Taking the direction of heat transfer Q to be into the working fluid and assuming a reversible mechanism, the heat is,
δQ = TδS
Where T denotes the temperature
S denotes the entropy.
Hence the change in internal energy formula thermodynamics is,
δU = TδS - PδV
Heat Capacity in Thermodynamics
Heat capacity, also known as thermal capacity, is a physical property of matter defined as the amount of heat required to cause a unit change in temperature in a given mass of a substance.
The joule per kelvin (J/K) is the SI unit of heat capacity.
The term "heat capacity" refers to a wide range of characteristics. The basic heat potential is the intense property that corresponds. The molar heat capacity is calculated by dividing the heat capacity by the volume of a substance in moles. The heat capacity per volume is measured by the volumetric heat capacity. Thermal mass is a term used in architecture and structural engineering to describe a building's heat capacity in thermodynamics.
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According to the first law of thermodynamics, heat supplied to the device contributes to both the work done and the change of internal energy at constant pressure.
The heat capacity is denoted by the letter C\[_{p}\].
Heat capacity at constant volume, dV = 0, dQ = dU (isochoric process)
The heat supplied The heat capacity in thermodynamic is an object, denoted by Q, hence the heat capacity equation is followed as,
C = \[\frac{\Delta Q}{\Delta T}\]
Where,
C: Heat capacity
\[\Delta\]Q: Total energy
\[\Delta\]T: Change in temperature
Heat capacities for a homogeneous system that is subjected to various thermodynamic processes.
Heat capacity at constant pressure, dQ = dU + PdV (Isobaric process)
would only add to the change in internal energy in a device performing a phase at constant volume and no work would be completed.
C\[_{v}\] is the heat capacity obtained in this manner. The value of Cv is never greater than the value of C\[_{p}\].
FAQs on Heat Capacity and Internal Energy Explained for Students
1. What is the fundamental difference between heat and internal energy in thermodynamics?
Heat and internal energy are related but distinct concepts. Internal energy (U) is the total energy stored within a system, representing the sum of the kinetic and potential energies of its molecules. It is a state function, meaning it depends only on the system's current state. Heat (Q), on the other hand, is the energy transferred between a system and its surroundings due to a temperature difference. Heat is energy in transit, not something a system 'has'.
2. What is heat capacity, and how does it differ from specific heat capacity?
Heat capacity (C) is a measure of the amount of heat energy required to raise the temperature of an entire object or substance by one degree Celsius (or one Kelvin). Its formula is C = Q / ΔT. Specific heat capacity (c) is an intrinsic property of a material. It is the amount of heat energy required to raise the temperature of one unit of mass (e.g., 1 kg or 1 g) of that material by one degree. The relationship is C = m × c, where 'm' is the mass of the substance.
3. What are Cp and Cv, and how do they relate to molar heat capacity?
Cp and Cv are types of molar heat capacity, which is the heat capacity per mole of a substance. They are particularly important for gases:
Cp (Molar heat capacity at constant pressure): The heat required to raise the temperature of one mole of a gas by 1K when its pressure is kept constant.
Cv (Molar heat capacity at constant volume): The heat required to raise the temperature of one mole of a gas by 1K when its volume is kept constant.
For an ideal gas, the relationship between them is given by Mayer's formula: Cp - Cv = R, where R is the universal gas constant.
4. How is the change in a system's internal energy (ΔU) related to its heat capacity at constant volume (Cv)?
The change in internal energy (ΔU) of an ideal gas is directly proportional to its change in temperature and is given by the formula ΔU = nCvΔT, where 'n' is the number of moles. This relationship holds true for any process (isobaric, isochoric, etc.), not just one at constant volume. This is because internal energy is a state function and depends only on temperature for an ideal gas. At constant volume, no work is done (W=0), so all heat supplied (Q) directly increases the internal energy (Q = ΔU).
5. Why is the molar heat capacity at constant pressure (Cp) always greater than at constant volume (Cv) for a gas?
Cp is always greater than Cv because of the work done by the gas.
At constant volume (Cv), all the heat supplied to the gas goes into increasing its internal energy (raising its temperature).
At constant pressure (Cp), the heat supplied must do two things: increase the internal energy (same amount as above for the same temperature rise) AND do work to expand the gas against the constant external pressure.
This extra energy required for doing work means more heat must be supplied at constant pressure to achieve the same 1K temperature rise, making Cp > Cv.
6. How does a system's internal energy change during a phase transition, like melting ice, when the temperature stays constant?
During a phase transition, the heat energy added (known as latent heat) does not increase the kinetic energy of the molecules, which is why the temperature remains constant. Instead, this energy is used to increase the potential energy of the molecules. It works against the intermolecular forces to break the bonds holding the substance in its solid (ice) or liquid (water) state. Therefore, even though the temperature is constant, the internal energy of the system increases significantly.
7. What is an example of heat capacity in a real-world scenario?
A classic example is water's high specific heat capacity. Water requires a large amount of heat energy to change its temperature. This is why:
Coastal areas have more moderate climates than inland areas. The large body of water absorbs a lot of heat in summer and releases it slowly in winter, stabilizing the temperature.
Water is used as a coolant in car engines. It can absorb a large amount of heat from the engine without its own temperature rising drastically.
