For an ideal gas, which of the following is true

Options

A. `((del E)/(del V))_(T) gt 0`
B. `((del P)/(del V))_(T)= 0`
C. `((del E)/(del V))_(T)= 0`
D. `((del (PV))/(del V))_(T) gt 0`

Explanation

To determine which statement is true for an ideal gas, we can analyze the properties of ideal gases based on the principles of thermodynamics. Here’s a step-by-step solution:

### Step 1: Understand the Characteristics of an Ideal Gas
An ideal gas is a theoretical gas composed of many particles that are in constant random motion. The following assumptions are made:
- The gas molecules do not attract or repel each other.
- The volume of the gas molecules is negligible compared to the volume of the container.
- Collisions between gas molecules and with the walls of the container are perfectly elastic.

### Step 2: Internal Energy of an Ideal Gas
The internal energy (U) of an ideal gas is a function of temperature only. For an ideal gas, the internal energy does not depend on volume or pressure. This means that if the temperature remains constant, the internal energy remains constant regardless of changes in volume.

### Step 3: Change in Internal Energy with Volume
At constant temperature (isothermal conditions), if the volume of an ideal gas changes, there is no change in internal energy. This is because:
- There are no intermolecular forces acting between the gas molecules.
- Therefore, no work is done on or by the gas during an isothermal expansion or compression.

### Step 4: Conclusion
Since the internal energy of an ideal gas remains constant during a change in volume at constant temperature, we can conclude that:
- The change in internal energy (ΔU) with respect to volume (ΔV) at constant temperature is zero.

Thus, the correct statement is:
**ΔU/ΔV at constant temperature = 0 for an ideal gas.**

### Final Answer
The correct option is that there is no change in internal energy with change in volume at constant temperature for an ideal gas.

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