An ideal gas is expanded isothermally at 300 K from 1 litre to 10 litres. Find the ΔE for this process (R = 2 cal mol⁻¹ K⁻¹)

The correct option is "zero".

To understand why the change in internal energy ($\mathrm{\Delta E}$ or $\mathrm{\Delta U}$) is zero, let us look at the thermodynamic properties of an ideal gas.

For an ideal gas, the internal energy is a function of temperature only. Mathematically, this is expressed as:
$E=f\left(T\right)$
where $E$ is the internal energy and $T$ is the absolute temperature.

The change in internal energy for $n$ moles of an ideal gas during any process is given by the formula:
$\mathrm{\Delta E}=n{C}_v\mathrm{\Delta T}$
where $C_v$ is the molar heat capacity at constant volume, and $\mathrm{\Delta T}$ is the change in temperature ($\mathrm{\Delta T}=T_{\mathrm{final}}-T_{\mathrm{initial}}$).

In this problem, the gas is expanded isothermally. An isothermal process is one that occurs at a constant temperature. Therefore:
$T=300\text{K}=\text{constant}$
Consequently, the change in temperature is:
$\mathrm{\Delta T}=0$

Substituting $\mathrm{\Delta T}=0$ into the internal energy equation:
$\mathrm{\Delta E}=n{C}_v\left(0\right)=0$

Therefore, the change in internal energy ($\mathrm{\Delta E}$) for this isothermal expansion of an ideal gas is indeed zero.