Question

For an ideal gas, which of the following thermodynamic quantities depends only on temperature?

• A. Enthalpy
• B. Entropy
• C. Gibbs free energy
• D. Pressure

Hint:

Remember that for real gases, enthalpy depends on both pressure and temperature due to intermolecular interactions.
For ideal gases, always look for \( U \) and \( H \) as temperature-dependent functions.

Answer 1

The Correct Option is A

An ideal gas is a theoretical gas composed of many randomly moving point particles that interact only through elastic collisions. The properties of an ideal gas depend on its state variables, such as temperature, volume, and pressure. For the given question, we need to identify which thermodynamic quantity depends solely on temperature.

1. Enthalpy: The enthalpy H of an ideal gas is defined as H = U + PV, where U is the internal energy and PV\) is the product of pressure and volume. For an ideal gas, the internal energy \(U is a function of temperature alone. Therefore, the enthalpy of an ideal gas also depends solely on temperature.
2. Entropy: Although entropy is a state function, for an ideal gas, it depends on both temperature and volume (or pressure). Therefore, it is not solely dependent on temperature.
3. Gibbs Free Energy: Gibbs free energy G = H - TS depends on enthalpy H, temperature T, and entropy S. Since entropy is influenced by other factors besides temperature, Gibbs free energy cannot depend solely on temperature.
4. Pressure: Pressure is a state variable that depends on temperature, volume, and the number of moles of gas, as per the ideal gas law PV = nRT. Thus, it is not dependent only on temperature.

Based on the analysis above, enthalpy is the thermodynamic quantity that depends solely on temperature for an ideal gas.

Answer 2

Step 1: Understanding the Concept:
For an ideal gas, the intermolecular forces of attraction are negligible.
This leads to specific thermodynamic relationships where internal energy and enthalpy become state functions of temperature alone.
Step 2: Key Formula or Approach:
The definition of Enthalpy (\( H \)) is:
\[ H = U + PV \]
Where \( U \) is internal energy, \( P \) is pressure, and \( V \) is volume.
Step 3: Detailed Explanation:
According to Joule's Law for an ideal gas, the internal energy \( (U) \) is a function of temperature only, i.e., \( U = f(T) \).
Using the ideal gas equation:
\[ PV = nRT \]
Substituting this into the enthalpy equation:
\[ H = U(T) + nRT \]
Since both terms on the right side of the equation (\( U \) and \( nRT \)) are functions of temperature only, enthalpy \( (H) \) is also a function of temperature only for an ideal gas.
In contrast, Entropy (\( S \)) and Gibbs free energy (\( G \)) depend on both temperature and pressure (or volume) as they involve logarithmic terms of \( P \) or \( V \).
Step 4: Final Answer:
For an ideal gas, enthalpy is the quantity that depends only on temperature.