Change in internal energy in an isothermal process for ideal gas is

Options

A. Zero
B. (+) ve
C. (-) ve
D. Cannot be predicted

Answer

To solve the problem regarding the change in internal energy in an isothermal process for an ideal gas, we can follow these steps:

### Step 1: Understand the Concept of Internal Energy
Internal energy (U) of an ideal gas is a function of temperature. For an ideal gas, the internal energy is directly proportional to its temperature.

### Step 2: Define Isothermal Process
An isothermal process is one in which the temperature (T) of the system remains constant throughout the process.

### Step 3: Relate Internal Energy to Temperature
Since the internal energy of an ideal gas depends only on its temperature, if the temperature does not change (as in an isothermal process), the internal energy will also not change.

### Step 4: Apply the Formula for Change in Internal Energy
The change in internal energy (ΔU) can be expressed as:
\[ \Delta U = nC_v \Delta T \]
where:
- \(n\) is the number of moles,
- \(C_v\) is the molar heat capacity at constant volume,
- \(\Delta T\) is the change in temperature.

### Step 5: Analyze the Isothermal Condition
In an isothermal process, since the temperature remains constant, we have:
\[ \Delta T = 0 \]

### Step 6: Substitute into the Formula
Substituting \(\Delta T = 0\) into the equation for change in internal energy:
\[ \Delta U = nC_v \cdot 0 = 0 \]

### Conclusion
Thus, the change in internal energy (ΔU) in an isothermal process for an ideal gas is:
\[ \Delta U = 0 \]

### Final Answer
The change in internal energy in an isothermal process for an ideal gas is zero.

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