Question

According to the Joules law of a perfect gas, the internal energy is a function of

• A. pressure only
• B. absolute temperature only
• C. specific volume only
• D. absolute entropy only

Hint:

Joule's Law is a fundamental principle for ideal gases, stating that their internal energy depends solely on their absolute temperature. This is a direct consequence of the assumption that there are no intermolecular forces in an ideal gas, meaning its internal energy is purely kinetic and thus dependent only on temperature.

Answer 1

The Correct Option is B

Step 1: Understand Joule's Law for ideal gases.
Joule's law (also known as Joule's second law or Joule's law of ideal gases) states that the internal energy of a fixed amount of an ideal gas depends only on its temperature, not on its pressure or volume. This law was derived from experiments conducted by James Prescott Joule.
Step 2: Explain the implications of Joule's experiment.
In Joule's experiment, an insulated container with two chambers (one filled with gas, the other evacuated) connected by a valve was used. When the valve was opened, the gas expanded into the vacuum (free expansion). Joule observed that there was no significant temperature change in the gas after expansion, and no work was done and no heat was transferred to the surroundings.
According to the first law of thermodynamics, \( \Delta U = Q - W \). For this free expansion, \( Q = 0 \) and \( W = 0 \), hence \( \Delta U = 0 \).
Since the temperature of the gas did not change during the expansion, this implied that the internal energy of an ideal gas is independent of volume (and thus also pressure, given the ideal gas law relationship between P, V, and T).
Step 3: Conclude the functional dependence of internal energy for a perfect (ideal) gas.
Therefore, for a perfect gas (ideal gas), the internal energy \( U \) is solely a function of its absolute temperature \( T \).
Mathematically, for an ideal gas, \( U = U(T) \). This means \( dU = C_v dT \), where \( C_v \) is the specific heat at constant volume, which itself is constant for an ideal gas. The final answer is $\boxed{\text{2}}$.