The graph pressure versus temperature (T) at constant volume is a straight line.(T/F)

Explanation

To determine whether the statement "The graph of pressure versus temperature at constant volume is a straight line" is true or false, 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
- \( V \) = volume
- \( n \) = number of moles of gas
- \( R \) = universal gas constant
- \( T \) = temperature

### Step 2: Analyze the Condition of Constant Volume
In this scenario, we are considering a situation where the volume \( V \) is held constant. This means that any changes in pressure \( P \) will be directly related to changes in temperature \( T \).

### Step 3: Rearranging the Ideal Gas Law
Since volume is constant, we can rearrange the Ideal Gas Law to express pressure in terms of temperature:
\[ P = \frac{nR}{V} T \]
Here, \( \frac{nR}{V} \) is a constant (let's call it \( k \)):
\[ P = kT \]

### Step 4: Interpret the Relationship
The equation \( P = kT \) shows that pressure \( P \) is directly proportional to temperature \( T \) when volume is constant. This indicates a linear relationship between pressure and temperature.

### Step 5: Graphical Representation
If we plot pressure \( P \) on the y-axis and temperature \( T \) on the x-axis, the graph will be a straight line passing through the origin, with a slope equal to the constant \( k \).

### Conclusion
Since we have established that pressure is directly proportional to temperature at constant volume, the statement "The graph of pressure versus temperature at constant volume is a straight line" is **True**.