Question

In an adiabatic process, no transfer of heat takes place between system and surroundings. Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following
A.$q=0$,$\mathrm{\Delta }T\ne 0$,$W=0$
B.$q\ne 0$,$\mathrm{\Delta }T=0$,$W=0$
C.$q=0$,$\mathrm{\Delta }T=0$,$W=0$
D.$q=0$,$\mathrm{\Delta }T<0$,$W\ne 0$

Answer 1

Hint:We know that an adiabatic process takes place without transferring heat or mass between a thermodynamic system and its surroundings. It supports the theory that is used to describe the first law of thermodynamics and is a major thermodynamic concept.

Complete step by step answer:For an adiabatic free expansion of an ideal gas, the gas is kept in an insulated container and then permitted to enlarge in a vacuum. Since there is no external pressure for the gas to enlarge against, the work done by or on the system is zero. Since this process does not involve any exchange of heat transfer or work, the first law of thermodynamics states that the net internal energy change of the system is zero. For an ideal gas, the temperature remains the same since the internal energy is dependent on temperature in that case.
For a free expansion, the work done will be zero.
$W=0$
For an adiabatic process, the heat will be zero.
$q=0$
So, from the first law of thermodynamics, the change in internal energy is the total of heat and the work done.
$\mathrm{\Delta }U=q+w$
Substituting the values of q and w, we get
$\mathrm{\Delta }U=q+w$
$\mathrm{\Delta }U=0+0$
$\mathrm{\Delta }U=0$
From the equation, we can see that there is no change in the internal energy, hence the temperature would also remain constant.
The equation is,
$\mathrm{\Delta }T=0$
Therefore, $W=0$, $q=0$ and $\mathrm{\Delta }T=0$ for free expansion of an ideal gas under adiabatic condition.
Therefore, Option (C) is correct.


Note:When the pressure of a gas is increased by work done on it by its surroundings, the process of adiabatic heating takes place. In the Earth's atmosphere when an air mass descends, the process of adiabatic heating occurs. Adiabatic cooling happens when the pressure on an adiabatically isolated system is reduced, permitting it to expand, thereby causing it to perform work on its surroundings.