Internal energy of an ideal gas depends on :-

Options

A. Volume
B. Temperature
C. Pressure
D. None of these

Answer

To determine how the internal energy of an ideal gas depends on certain parameters, we can follow these steps:

### Step 1: Understand Internal Energy
Internal energy (U) of a gas is defined as the total energy contained within the system, which includes both kinetic and potential energies of the particles. For an ideal gas, we primarily consider the kinetic energy.

### Step 2: Kinetic Energy of Gas Particles
The internal energy of an ideal gas is essentially the sum of the kinetic energies of all the gas particles. The kinetic energy (KE) of a single particle can be expressed as:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the particle and \( v \) is its velocity.

### Step 3: Relate Internal Energy to Temperature
For an ideal gas, the average kinetic energy of the particles is directly proportional to the absolute temperature (T) of the gas. This relationship can be expressed as:
\[ KE_{avg} = \frac{3}{2} kT \]
where \( k \) is the Boltzmann constant. Therefore, the total internal energy (U) for one mole of an ideal gas can be expressed as:
\[ U = n \cdot KE_{avg} = n \cdot \frac{3}{2} kT \]
where \( n \) is the number of moles.

### Step 4: Conclusion
From the above relationship, we can conclude that the internal energy of an ideal gas depends solely on the temperature (T) of the gas. Therefore, the correct answer is that the internal energy of an ideal gas depends on temperature.

### Final Answer
The internal energy of an ideal gas depends on the temperature of the gas.

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