Identify the characteristics of an adiabatic process in a monoatomic gas. (A) Internal energy is constant. (B) Work done in the process is equal to the change in internal energy. (C) The product of temperature and volume is a constant. (D) The product of pressure and volume is a constant. (E) The work done to change the temperature from $\mathrm{T}_1$ to $\mathrm{T}_2$ is proportional to $\left(\mathrm{T}_2-\mathrm{T}_1\right)$. Choose the correct answer from the options given below :

<p>In an adiabatic process, the key characteristics for a monoatomic gas are:</p> <p><p><strong>No Heat Exchange</strong>: The adiabatic process occurs without heat transfer, meaning $ Q = 0 $.</p></p> <p><p><strong>Work Done and Internal Energy Change</strong>: The work done on or by the system is equal to the change in internal energy. Mathematically, this is expressed as:</p> <p>$ \Delta U = -W $</p> <p>where $\Delta U$ is the change in internal energy and $W$ is the work done.</p></p> <p><p><strong>Work and Temperature Relationship</strong>: The work done when changing the temperature from $ T_1 $ to $ T_2 $ is proportional to the difference between these temperatures. This relationship can be expressed as:</p> <p>$ |\text{Work Done}| = nC_v \Delta T \propto (T_2 - T_1) $</p> <p>Here, $ n $ is the number of moles, $ C_v $ is the molar heat capacity at constant volume, and $\Delta T$ is the change in temperature.</p></p> <p>From these characteristics, the correct features of an adiabatic process in a monoatomic gas relate to the relationships involving work done and temperature change, specifically options (B) and (E).</p>