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# The temperature of the system decreases in the process of:A) Free expansionB) Adiabatic expansionC) Isothermal expansionD) Isothermal compression

Last updated date: 22nd Feb 2024
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Hint: In this question we are going to find the change in heat, work done, change in internal energy and change in temperature. We will use the first law of thermodynamics. Following is the mathematical expression of first law of thermodynamics-
$\Delta U = \Delta Q - \Delta W$

Option (A) is free expansion, in free expansion there will be no work done, so $\Delta W = 0$ and there will be no heat transfer, so $\Delta Q = 0$.
Hence, by using the first law of thermodynamics $\Delta U = 0$.
It implies that there will be no change in temperature. So, $\Delta T = 0$
The gas equation in adiabatic process is $P{V^\gamma } = {\text{ constant}}$
In adiabatic process $\Delta Q = 0$
Using first law of thermodynamics,
$\Rightarrow \Delta U = \Delta Q - \Delta W$
Putting$\Delta Q = 0$,
$\Rightarrow \Delta U = - \Delta W$……….(i)
Change in work done is given by,
$\Rightarrow \Delta W = \int {P\Delta V}$
Since it is an expansion process so the volume will increase, so $\Delta V > 0$
So, $\Delta W > 0$
From equation (i), we can see that change in internal energy will be negative. It means the internal energy will decrease.
Relation between internal energy and temperature is given by,
$\Rightarrow \Delta U = {C_V}\Delta T$
Where,
${C_V}$ is the specific heat at constant volume
By this formula we can see that as internal energy decreases the temperature will also decrease.
Option (C) is isothermal expansion, since this is an isothermal process so there will be no change in temperature.
Option (D) is isothermal compression, since this is an isothermal process so there will be no change in temperature.
Since the temperature decreases in adiabatic expansion.

So option (B) is correct.

Note: The change in heat is zero in adiabatic process but there will always be a change in temperature. Adiabatic processes are of two types-