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# in an isothermal change the internal energy of the ideal gas molecules

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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 Home Thermodynamics Properties of Gases

## 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

## Answer (Detailed Solution Below)

Option 3 : remains constant

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## Detailed Solution

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 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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Q1. Constant volume-specific heats of incompressible substances depend on ______.Q2. The pressure p of gas in terms of its means kinetic energy per unit volume E is equal toQ3. Which of the following properties of a composite material can be computed by means of a rule of mixtures? I) Mass II) Volume III) Density IV) Melting pointQ4. According to the kinetic theory of gases, the absolute zero temperature is attained whenQ5. Which of the following gas leaked in the Bhopal Gas tragedy in December 1984?Q6. The difference between two specific heats,

Cp−Cv=RJ

. This relation is valid for

Q7. A perfect gas at 27°C is heated at constant pressure till its volume is double. The final temperature isQ8. The isothermal process is associated with:Q9. For which of the following substances, the internal energy and enthalpy are the functions of temperature onlyQ10. The colour of hydrogen is ___________.

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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

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## 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

## Join The Discussion

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## Isothermal process ## Isothermal process

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

Thermodynamics

The classical Carnot heat engine

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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.}

## Contents

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

## Etymology

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

## Examples

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). 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. Phase changes, such as melting or evaporation, are also isothermal processes when, as is usually the case, they occur at constant pressure. 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. 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. 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.

In the isothermal compression of a gas there is work done on the system to decrease the volume and increase the pressure. 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. Thus, specifying that a process is isothermal is not sufficient to specify a unique process.

## Details for an ideal gas 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 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. 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

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

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

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