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    [Solved] In an isothermal process, the internal energy of gas molecul

    Explanation: The internal energy of a system is the energy contained within the system, including the kinetic and potential energy as a whole. The internal en

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    In an isothermal process, the internal energy of gas molecules ________.

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    increases decreases remains constant

    may increase/decrease depending on the properties of gas

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    Option 3 : remains constant

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    The internal energy of a system is the energy contained within the system, including the kinetic and potential energy as a whole.

    The internal energy of an ideal gas is a function of absolute temperature only.

    For an ideal gas:

    U = f(T) only

    Change in internal energy is given as

    U2 - U1 = mcv(T2 - T1)

    T2 = T1 ⇒ U2 = U1

    In case of isothermal process, there is no change in temperature so the change in internal energy is also zero. So internal energy of the system remains constant.

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    In an isothermal process the internal energy of gas molecules

    In an isothermal process, the internal energy of gas molecules a) Increases b) Decreases c) Remain constant d) May increase/decrease depending on the properties of gas

    In an isothermal process the internal energy of gas molecules

    Home / Mechanical Engineering / Engineering Thermodynamics / Question


    In an isothermal process, the internal energy of gas molecules

    A. Increases B. Decreases C. Remain constant

    D. May increase/decrease depending on the properties of gas

    Answer: Option C

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    Isothermal process

    Isothermal process

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    "Isothermal" redirects here. For other uses, see Isotherm.


    The classical Carnot heat engine

    show Branches show Laws show Systems show System properties show Material properties show Equations show Potentials show HistoryCulture show Scientists show Other Category vte

    In thermodynamics, an isothermal process is a type of thermodynamic process in which the temperature of a system remains constant: Δ = 0. This typically occurs when a system is in contact with an outside thermal reservoir, and a change in the system occurs slowly enough to allow the system to be continuously adjusted to the temperature of the reservoir through heat exchange (see quasi-equilibrium). In contrast, an is where a system exchanges no heat with its surroundings ( = 0).

    Simply, we can say that in an isothermal process

    {\displaystyle T={\text{constant}}}

    {\displaystyle \Delta T=0}

    {\displaystyle dT=0}

    For ideal gases only, internal energy

    {\displaystyle \Delta U=0}

    while in adiabatic processes:

    {\displaystyle Q=0.}


    1 Etymology 2 Examples

    3 Details for an ideal gas

    4 Calculation of work

    5 Example of an isothermal process

    6 Entropy changes 7 See also 8 References


    The adjective "isothermal" is derived from the Greek words "ἴσος" ("isos") meaning "equal" and "θέρμη" ("therme") meaning "heat".


    Isothermal processes can occur in any kind of system that has some means of regulating the temperature, including highly structured machines, and even living cells. Some parts of the cycles of some heat engines are carried out isothermally (for example, in the Carnot cycle).[1] In the thermodynamic analysis of chemical reactions, it is usual to first analyze what happens under isothermal conditions and then consider the effect of temperature.[2] Phase changes, such as melting or evaporation, are also isothermal processes when, as is usually the case, they occur at constant pressure.[3] Isothermal processes are often used and a starting point in analyzing more complex, non-isothermal processes.

    Isothermal processes are of special interest for ideal gases. This is a consequence of Joule's second law which states that the internal energy of a fixed amount of an ideal gas depends only on its temperature.[4] Thus, in an isothermal process the internal energy of an ideal gas is constant. This is a result of the fact that in an ideal gas there are no intermolecular forces.[4] Note that this is true only for ideal gases; the internal energy depends on pressure as well as on temperature for liquids, solids, and real gases.[5]

    In the isothermal compression of a gas there is work done on the system to decrease the volume and increase the pressure.[4] Doing work on the gas increases the internal energy and will tend to increase the temperature. To maintain the constant temperature energy must leave the system as heat and enter the environment. If the gas is ideal, the amount of energy entering the environment is equal to the work done on the gas, because internal energy does not change. For isothermal expansion, the energy supplied to the system does work on the surroundings. In either case, with the aid of a suitable linkage the change in gas volume can perform useful mechanical work. For details of the calculations, see calculation of work.

    For an adiabatic process, in which no heat flows into or out of the gas because its container is well insulated,  = 0. If there is also no work done, i.e. a free expansion, there is no change in internal energy. For an ideal gas, this means that the process is also isothermal.[4] Thus, specifying that a process is isothermal is not sufficient to specify a unique process.

    Details for an ideal gas[edit]

    Figure 1. Several isotherms of an ideal gas on a p-V diagram, where p for pressure and V the volume.

    For the special case of a gas to which Boyle's law[4] applies, the product ( for gas pressure and for gas volume) is a constant if the gas is kept at isothermal conditions. The value of the constant is , where is the number of moles of the present gas and is the ideal gas constant. In other words, the ideal gas law  =  applies.[4] Therefore:

    {\displaystyle p={nRT \over V}={{\text{constant}} \over V}}

    holds. The family of curves generated by this equation is shown in the graph in Figure 1. Each curve is called an isotherm, meaning a curve at a same temperature . Such graphs are termed indicator diagrams and were first used by James Watt and others to monitor the efficiency of engines. The temperature corresponding to each curve in the figure increases from the lower left to the upper right.

    Calculation of work[edit]

    Figure 2. The purple area represents the work for this isothermal change.

    In thermodynamics, the reversible work involved when a gas changes from state to state is[6]

    {\displaystyle W_{A\to B}=-\int _{V_{A}}^{V_{B}}p\,dV}

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