Question

Reversible expansion of an ideal gas under isotheramal and adiabatic conditions are as shown in the figure.
AB $\to$ Isothermal expansion
AC $\to$ Adiabatic expansion

Which of the following options is not correct?

• A. $\Delta S_{isothermal}>\Delta S_{adiabatic}$
• B. $T_A=T_B$
• C. $W_{isothermal}>W_{adiabatic}$
• D. $T_C>T_A$

Answer 1

The correct option is D $T_C>T_A$

For an ideal gas, internal energy is a function of temperature. Final temperature i.e., $T_C$ for adiabatic process is less than its initial temperature i.e., $T_A$
In a adiabatic expansion, the work to expand the gas comes at the expense of the gas or to be particular the kinetic energy of the gas. The kinetic energy of gas in statistical mechanics can be written as:

K.E. = nkT, where n depends on the degree of freedom. Thus, as the gas expands, kinetic energy of the gas decreases, and the temperature decreases.
$\therefore T_C<T_A$