Under which of the following conditions PV=RT is obeyed most closely by a real gas ?

Options

A. high pressure and high temperature
B. low pressure and low temperature
C. low pressure and high temperature
D. high pressure and low temperature

Answer

To determine under which conditions the equation PV = RT is obeyed most closely by a real gas, we can follow these steps:

### Step 1: Understand the Ideal Gas Law
The equation PV = RT represents the ideal gas law, where:
- P = Pressure of the gas
- V = Volume of the gas
- R = Universal gas constant
- T = Temperature of the gas in Kelvin

### Step 2: Recognize the Behavior of Real Gases
Real gases do not always behave like ideal gases. The ideal gas law is an approximation that holds under certain conditions.

### Step 3: Identify Conditions for Ideal Behavior
Real gases tend to behave more like ideal gases under specific conditions:
- **Low Pressure**: At low pressures, the volume of the gas particles becomes negligible compared to the volume of the container, and intermolecular forces have less effect.
- **High Temperature**: At high temperatures, the kinetic energy of the gas particles increases, which reduces the effect of intermolecular forces.

### Step 4: Conclusion
Therefore, a real gas behaves most like an ideal gas (and thus obeys PV = RT most closely) when both:
- The pressure is low
- The temperature is high

### Final Answer
The correct condition under which PV = RT is obeyed most closely by a real gas is **low pressure and high temperature**.

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