Internal energy of an ideal gas changes with change in its

Options

A. Pressure only
B. Volume only
C. Temperature only
D. Temperature and pressure

Answer

To determine how the internal energy of an ideal gas changes, we can follow these steps:

### Step 1: Understand Internal Energy
The internal energy (U) of an ideal gas is a measure of the total kinetic energy of the gas particles. For an ideal gas, this energy depends primarily on the temperature of the gas.

### Step 2: Use the Formula for Internal Energy
The internal energy of an ideal gas can be expressed using the formula:
\[ U = \frac{f}{2} nRT \]
where:
- \( U \) is the internal energy,
- \( f \) is the degree of freedom of the gas molecules,
- \( n \) is the number of moles of the gas,
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature of the gas.

### Step 3: Analyze the Variables
In the formula, \( f \), \( n \), and \( R \) are constants for a given gas under specific conditions. The only variable that can change is the temperature \( T \).

### Step 4: Determine the Relationship
Since \( U \) is directly proportional to \( T \) (as \( f \), \( n \), and \( R \) are constants), we can conclude that:
\[ U \propto T \]
This means that any change in temperature will result in a change in internal energy.

### Step 5: Conclusion
Thus, the internal energy of an ideal gas changes with a change in its temperature.

### Final Answer
The internal energy of an ideal gas changes with a change in its **temperature**.

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