Question

Identify the correct statements from the following. (i). For adiabatic process, $\Delta U = W_{adiabatic$} (ii). Work is a path function. (iii). Volume is an extensive property.

• A. i, ii, iii
• B. i, iii only
• C. ii, iii only
• D. i, ii only

Hint:

First Law of Thermodynamics: $\Delta U = q + W$ (where $W$ is work done on the system).
Adiabatic process: $q=0$, so $\Delta U = W_{on\_system}$ or $\Delta U = -W_{by\_system}$.
Path functions (e.g., work, heat) depend on the path taken. State functions (e.g., $\Delta U, \Delta H, \Delta S, P, V, T$) depend only on the initial and final states.
Extensive properties (e.g., volume, mass, moles, energy) depend on the amount of substance.
Intensive properties (e.g., pressure, temperature, density, molar properties) do not depend on the amount of substance.

Answer 1

The Correct Option is A

Let's analyze each statement: (i). For adiabatic process, $\Delta U = W_{adiabatic$} The first law of thermodynamics states that $\Delta U = q + W$, where $\Delta U$ is the change in internal energy, $q$ is the heat added to the system, and $W$ is the work done on the system. (Note: Some conventions use $W$ as work done *by* the system, then $\Delta U = q - W_{by\_system}$). Let's use $W$ as work done *on* the system. An adiabatic process is one in which no heat is exchanged between the system and its surroundings, i.e., $q=0$. Substituting $q=0$ into the first law: $\Delta U = 0 + W_{adiabatic} \Rightarrow \Delta U = W_{adiabatic}$. If the convention $W$ is work done *by* the system, then $W_{by\_system} = -W_{on\_system}$. So $\Delta U = q - W_{by\_system}$. For adiabatic, $\Delta U = -W_{by\_system, adiabatic}$. The statement given is $\Delta U = W_{adiabatic}$. This is true if $W_{adiabatic}$ refers to work done *on* the system. If it refers to work done *by* the system, then $\Delta U = -W_{adiabatic}$. Commonly, in physics texts $W$ is work done on the system, while in some chemistry/engineering contexts $W$ is work done by the system. Assuming $W_{adiabatic}$ means work done *on* the system, statement (i) is correct. If the statement meant $W_{by\_system}$, it should be $\Delta U = -W$. Given the options, it's likely the convention $\Delta U = q+W_{on}$ is used. (ii). Work is a path function. Work ($W$) and heat ($q$) are path functions. This means their values depend on the specific path taken between the initial and final states of a thermodynamic process, not just on the states themselves. State functions, like internal energy ($U$), enthalpy ($H$), entropy ($S$), Gibbs free energy ($G$), depend only on the initial and final states. So, statement (ii) is correct. (iii). Volume is an extensive property. Thermodynamic properties can be classified as intensive or extensive. \begin{itemize} \item Extensive properties depend on the amount of matter in the system (e.g., mass, volume, internal energy, enthalpy, entropy). If you double the amount of substance, an extensive property doubles. \item Intensive properties do not depend on the amount of matter (e.g., temperature, pressure, density, concentration, molar volume). \end{itemize} Volume ($V$) depends on the amount of substance. If you have twice the amount of gas at the same temperature and pressure, it occupies twice the volume. So, statement (iii) is correct. Since all three statements (i), (ii), and (iii) are correct (assuming the standard physics convention for work in statement i), option (a) is the correct choice. \[ \boxed{\text{i, ii, iii}} \]