Animated Solution for Physics - Thermodynamics: Which of the following statements is correct for any thermodynamic system?

This question tests your fundamental understanding of thermodynamic properties and processes. Let's break down each option to see why it is either correct or incorrect.

Let's start by looking at option (a): "The internal energy changes in all processes." We know that for an ideal gas, the internal energy $U$ is a function of temperature $T$ only. If we consider an isothermal process, the temperature remains constant throughout the process ($\Delta T=0$). Consequently, the change in internal energy is also zero ($\Delta U=0$). Therefore, internal energy does not change in all processes, making this statement false.

Next, let's examine option (c): "The change in entropy can never be zero." Entropy $S$ is a measure of the disorder or randomness of a system. The change in entropy for a reversible process is given by $\Delta S=\frac{\Delta Q}{T}$. In a reversible adiabatic process, there is no heat exchange with the surroundings, meaning $\Delta Q=0$. Plugging this into our formula, we get $\Delta S=0$. Such a process is also called an isentropic process. Thus, the change in entropy can be zero, making this statement false.

Now, let's look at option (d): "The work done in an adiabatic process is always zero." According to the first law of thermodynamics, $\Delta Q=\Delta U+W$. For an adiabatic process, we know $\Delta Q=0$. Substituting this into the first law gives us $0=\Delta U+W$, which simplifies to $W=-\Delta U$. This means that the work done by the system is equal to the decrease in its internal energy. As long as the temperature of the gas changes during the adiabatic expansion or compression, $\Delta U$ will be non-zero, and therefore the work done $W$ will also be non-zero. Hence, this statement is false.

Finally, let's evaluate option (b): "Internal energy and entropy are state functions." In thermodynamics, properties are classified into two categories: state functions and path functions. A state function is a property whose value depends only on the current state of the system (characterized by variables like pressure $P$, volume $V$, and temperature $T$) and is completely independent of the path taken to reach that state.

Both internal energy ($U$) and entropy ($S$) are classic examples of state functions. If a system goes from state A to state B, the change in internal energy ($\Delta U=U_B-U_A$) and the change in entropy ($\Delta S=S_B-S_A$) will be exactly the same regardless of whether the process was isothermal, adiabatic, isobaric, or any complex combination of paths.

Conversely, heat ($Q$) and work ($W$) are path functions because their values depend heavily on the specific thermodynamic path taken between the initial and final states. Therefore, option (b) is the only correct statement.