Question

In an isothermal expansion of ideal gas:
A. Internal energy decreases
B. Internal energy increases
C. Complete energy decreases
D. Internal energy remains constant

Answer 1

Hint: You should see the word “isothermal” to get a clear idea. An isothermal process is a change of a system, in which the temperature remains constant:$\Delta T$ =0.

Complete step by step answer:

As we already know, an isothermal process is a change of a system, in which the temperature remains constant.
Internal energy is a function of temperature because internal energy of ideal gas comprises of molecular kinetic energy which further depends on the temperature and
$\Delta U$ = $C_{ v }dT$
Hence, for the isothermal process, dT=0, then $\Delta U$=0
Therefore, we can conclude that the correct answer to this question is option D.

Additional information:
For an ideal gas during an isothermal expansion the enthalpy, as well as internal energy, remains constant.
During isothermal expansion of an ideal gas, $\Delta E$ = 0, $\Delta T$=0
From the definition of enthalpy
H = E + PV
$\Rightarrow$ $\Delta $H = $\Delta $E + $\Delta $(PV)
$\Rightarrow$ $\Delta $H = $\Delta $E + $\Delta $(nRT) {Since, PV=nRT for an ideal gas}
$\Rightarrow$ $\Delta $H = $\Delta $E + nR$\Delta $T (because n and R are constant)
Since we already know value of $\Delta $E and $\Delta $T is 0
Therefore, we can write $\Delta $H=0

Note: You should also know about two cases where the isothermal process may not have a change in internal energy as zero:
In the case of real gas, some of the supplied energy may be converted to potential energy. So, while there is no change in temperature internal energy may still change.
In the case of phase change, the process is isothermal but internal energy increases/decreases. This is due to the increase/decrease in degrees of freedom.