The graph between (P/T) and T for a gas at constant volume will be:

Options

A.
B.
C.
D.

Explanation

To solve the question regarding the graph between (P/T) and T for a gas at constant volume, we can follow these steps:

### Step 1: Understand the Ideal Gas Law
The ideal gas law is given by the equation:
\[ PV = nRT \]
where:
- \( P \) = pressure of the gas
- \( V \) = volume of the gas
- \( n \) = number of moles of the gas
- \( R \) = ideal gas constant
- \( T \) = temperature of the gas in Kelvin

### Step 2: Rearrange the Ideal Gas Law
At constant volume, we can rearrange the ideal gas law to express pressure in terms of temperature:
\[ P = \frac{nRT}{V} \]

### Step 3: Divide Pressure by Temperature
To find the relationship between \( P/T \) and \( T \), we divide both sides of the equation by \( T \):
\[ \frac{P}{T} = \frac{nR}{V} \]

### Step 4: Analyze the Equation
From the equation \( \frac{P}{T} = \frac{nR}{V} \), we can see that:
- \( \frac{P}{T} \) is constant at constant volume (since \( n \) and \( R \) are constants, and \( V \) is also constant).
- This shows that \( \frac{P}{T} \) does not depend on \( T \).

### Step 5: Graphical Representation
Since \( \frac{P}{T} \) is constant, the graph of \( \frac{P}{T} \) versus \( T \) will be a horizontal line. This means that as temperature increases, the value of \( \frac{P}{T} \) remains the same.

### Conclusion
The correct graph between \( \frac{P}{T} \) and \( T \) for a gas at constant volume is a horizontal line along the x-axis.

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