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In thermodynamics, an adiabatic process or an isocaloric process is a process in which no heat is transferred to or from working fluid. The term "adiabatic" literally means an absence of heat transfer; for example, an adiabatic boundary is a boundary that is impermeable to heat transfer and the system is said to be adiabatically (or thermally) insulated. An insulated wall approximates an adiabatic boundary. Another example is the adiabatic flame temperature, which is the temperature that would be achieved by a flame in the absence of heat loss to the surroundings. An adiabatic process which is also reversible is called an isotropic process.

Ideal gas:

For a simple substance, during an adiabatic process in which the volume increases, the internal energy of the working substance must necessarily decrease. The mathematical equation for an ideal fluid undergoing an adiabatic process is,

p.v^( γ )

where P is pressure, V is volume, and

γ =CP/CV=α +1 / α .

CP being the molar specific heat for constant pressure and CV being the molar specific heat for constant volume. α comes from the number of degrees of freedom divided by 2 (3/2 for monotonic gas, 5/2 for diatomic gas). For a monotonic ideal gas, γ = 5 / 3, and for a diatomic gas (such as nitrogen and oxygen, the main components of air) γ = 7 / 5. Note that the above formula is only applicable to classical ideal gases and not Bose-Einstein or Fermi gases.

For the derivation of work done in an adiabatic process, please visit the link I added below.

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Q: Derivation for workdone in isothermal process?
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In a reversible isothermal expansion process the fluid expands from 10 bar and 2 meter cube to 2 bar and 10 meter cube during the process the heat supplied is 100 KWwhat is the workdone?

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What isothermal process?

Isothermal process is a process in which change in pressure and volume takes place at a constant temperature.


What is true about isothermal process?

An isothermal process is one in which the temperature remains constant throughout. This means that the internal energy of the system remains constant as well. In an isothermal process, the heat added to or removed from the system is balanced by the work done by or on the system.


Which of the following is true of an isothermal process Temperature is constant W equals Q ΔU equals 0 Pressure is constant?

Temperature is constant during an isothermal process. The work done (W) is equal to the heat added (Q). The change in internal energy (ΔU) is zero for an isothermal process. The pressure can vary during an isothermal process, depending on the specific conditions.


What is energy is transferred to a gas as heat and work If there is no change in its internal energy the process is known as?

The process is known as an isothermal process. In an isothermal process, the energy transferred to the gas as heat and work results in no change in the gas's internal energy because the temperature remains constant throughout the process.


What are examples of isothermal process?

An isothermal process is a change in a system where the temperature stays constant (delta T =0). A practical example of this is some heat engines which work on the basis of the carnot cycle. The carnot cycle works on the basis of isothermal.


What are the characteristics of isothermal process?

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How does the volume change in an isentropic process?

The entropy of an ideal gas during an isothermal process may change because normally the entropy is a net zero. The change of on isothermal process can produce positive energy.


What statement best describe the isothermal process?

An isothermal process is one where the temperature remains constant throughout. This means that the internal energy of the system stays the same, as the heat transfer into the system is balanced by the work done by the system. In an ideal gas, this results in no change in the pressure or volume during an isothermal process.


What is isothermal?

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What is the difference between isothermal and hyperbolic process?

An isothermal process is one where the temperature remains constant throughout the process, while a hyperbolic process refers to a mathematical curve represented by a hyperbola. In the context of thermodynamics, an isothermal process typically involves heat exchange to maintain constant temperature, while a hyperbolic process is not a specific thermodynamic process but rather a mathematical representation.


Is the work-done in isothermal system is zero why?

In an isothermal process, the temperature of the system remains constant. Since work done is the result of a change in energy, and the temperature does not change, there is no transfer of energy in the form of work during an isothermal process. Thus, the work done in an isothermal system is zero.