For a constant volume gas thermometer, one should fill the gas at

Options

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

Answer

To solve the question regarding the conditions under which one should fill the gas in a constant volume gas thermometer, we can follow these steps:

### Step 1: Understand the Principle of a Constant Volume Gas Thermometer
A constant volume gas thermometer operates on the principle that the pressure of a gas is directly proportional to its temperature when the volume is held constant. This relationship is derived from the ideal gas law, which states:

\[ PV = nRT \]

Where:
- \( P \) = pressure
- \( V \) = volume
- \( n \) = number of moles of gas
- \( R \) = ideal gas constant
- \( T \) = temperature in Kelvin

### Step 2: Simplify the Ideal Gas Law for Constant Volume
Since the volume \( V \) is constant in a gas thermometer, we can rearrange the ideal gas law to focus on the relationship between pressure and temperature:

\[ P = \frac{nR}{V} \cdot T \]

Here, \( \frac{nR}{V} \) is a constant when the volume and the amount of gas are fixed.

### Step 3: Identify the Conditions for Ideal Gas Behavior
For a gas to behave ideally, it should be at high temperature and low pressure. Under these conditions, the interactions between gas molecules are minimized, and the gas behaves more like an ideal gas.

### Step 4: Analyze the Options Given
Now, let's analyze the options provided:
- **Option A:** Low temperature and low pressure
- **Option B:** Low temperature and high pressure
- **Option C:** High temperature and low pressure
- **Option D:** High temperature and high pressure

Since we established that we need high temperature and low pressure for the gas to behave ideally, the correct option is:

**Option C: High temperature and low pressure.**

### Final Answer
One should fill the gas in a constant volume gas thermometer at high temperature and low pressure.

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