Internal energy of an ideal gas change`s with change in its

Options

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

Answer

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

### Step-by-Step Solution:

1. **Understand the Concept of Internal Energy**:
- The internal energy (U) of an ideal gas is a measure of the total kinetic energy of the gas molecules. For an ideal gas, the internal energy is primarily a function of temperature.

2. **Use the Formula for Internal Energy**:
- The change in internal energy (ΔU) can be expressed using the formula:
\[ \Delta U = \frac{F}{2} nR \Delta T \]
- Here, \(F\) is the degrees of freedom of the gas, \(n\) is the number of moles, \(R\) is the universal gas constant, and \(\Delta T\) is the change in temperature.

3. **Identify the Variables**:
- From the formula, we can see that:
- \(F\) (degrees of freedom) is constant for a given type of gas.
- \(n\) (number of moles) is also constant if the amount of gas does not change.
- \(R\) is a constant value for all ideal gases.
- \(\Delta T\) is the variable that influences the change in internal energy.

4. **Conclude the Dependency**:
- Since the internal energy is directly proportional to the change in temperature (\(\Delta T\)), we can conclude that the internal energy of an ideal gas changes with a change in its temperature.

5. **Select the Correct Option**:
- Based on the analysis, the correct answer to the question is that 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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