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

Options

A.
B.
C.
D.

Explanation

To solve the problem of determining the graph between \( \frac{P}{T} \) 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 \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is the temperature.

### Step 2: Identify the Given Condition
In this problem, we are told that the volume \( V \) is constant. This means that for a given amount of gas, the number of moles \( n \) and the gas constant \( R \) are also constant.

### Step 3: Rearranging the Ideal Gas Law
Since \( V \) is constant, we can rearrange the ideal gas law to express pressure \( P \) in terms of temperature \( T \):
\[ P = \frac{nRT}{V} \]

### Step 4: Express \( \frac{P}{T} \)
Now, we can express \( \frac{P}{T} \):
\[ \frac{P}{T} = \frac{nR}{V} \]
This shows that \( \frac{P}{T} \) is constant because \( n \), \( R \), and \( V \) are all constants.

### Step 5: Graphing \( \frac{P}{T} \) against \( T \)
Since \( \frac{P}{T} \) is constant, when we plot \( \frac{P}{T} \) on the y-axis against \( T \) on the x-axis, we will get a horizontal line. This indicates that regardless of the temperature \( T \), the value of \( \frac{P}{T} \) remains the same.

### Conclusion
Thus, the graph between \( \frac{P}{T} \) and \( T \) for a gas at constant volume will be a horizontal line.

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