Question

Explain:

What is Adiabatic. Give the expression of Adiabatic and what is the difference between the graph of Adiabatic and isothermal.


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Answer 1

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Adiabatic means there is no heat exchange between the system and the surrounding.

• Adiabatic means there is no heat exchange between the system and the surrounding, therefore, the temperature will increase if it is a compression, or temperature will decrease in expansion.

• Isothermal means, there is no temperature change; thus, the temperature in a system is constant. This is acquired by changing the heat.

• In adiabatic dQ=0, but dT≠0. However, in isothermal changes dT=0 and dQ ≠0.

• Adiabatic changes take place rapidly, whereas isothermal changes take place very slowly.

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Answer 2

$\huge{\textbf{\underline{Adiabatic\;Process}}}$

★What is Adiabatic process?

⟹An adiabatic process occurs without transfer of heat or mass of substances between a thermodynamic system and its surroundings. In an adiabatic process, energy is transferred to the surroundings only as work.

• If work is done on the system, internal energy increases.
• dU = – dW
• If work is done by the system, internal energy decreases.
• – dU = dW

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$\huge{\textbf{\underline{Expression\;For\;Adiabatic\;Process}}}$

According to the first law of thermodynamics.

Q = dU + dW

In Adiabatic process

Q = 0

dW = – dU

But, dU = CvdT

∴ dW = CvdT

The total work done when one mole of a gas expands adiabatically from temperature T1 to temperature T2 is given by,

$W = \int dW = - { \int}^{T2}_{T1} \:CvdT \\ = - Cv { \int}^{T2}_{T1} dT \\ On \: integrating... \\ = - Cv \: ({T})^{T2}_{T1}$

–Cv [T2 – T1]

W = Cv [T2 – T1]

W = Cv [T1 – T2] ———> ①

We have Cp – Cv = R ———> ②

Where, Cp is the molar specific heat at constant pressure and R is the universal gas constant.

Dividing both sides of eqtn ② by Cv

$\frac{Cp - Cv}{Cv} = \frac{R}{Cv} \\ \frac{Cp}{Cv} - 1 = \frac{R}{Cv} \\ Cv = \frac{R}{ \frac{Cp}{Cv} - 1 } \\ Cv = \frac{R}{\gamma - 1} \: (where \: \gamma = \frac{Cp}{Cv})$

On substituting Cv value in eqtn ①

$W = \frac{R}{ \gamma - 1}(T1 - T2) \: (for \: 1 \: mole) \\ W = \frac{nR}{ \gamma - 1}(T1 - T2)$

When the gas expands adiabatically work is done by the gas.

So, W is +ve.

∴ T2 < T1

There is a decrease in temperature.

There is a decrease in temperature. When the gas is compressed adiabatically work is done on the gas.

So, W is –ve

∴ T2 > T1

There is a increase in temperature.

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Difference between the graph of Adiabatic and isothermal

Note:- Kindly please look into the graph given in the attachment.

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