Which of the following will give a linear plot at constant pressure ?

Options

A. V vs T
B. V vs 1/T
C. T vs 1/V
D. None of these

Explanation

To determine which of the following will give a linear plot at constant pressure, we can apply Charles's Law. Here’s a step-by-step solution:

### Step 1: Understand Charles's Law
Charles's Law states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature (in Kelvin). Mathematically, it can be expressed as:
\[ V \propto T \]
or
\[ V = kT \]
where \( V \) is the volume, \( T \) is the temperature, and \( k \) is a constant.

### Step 2: Identify the Variables
In this case, we are looking for a relationship between volume (V) and temperature (T) that will yield a linear graph. The linear relationship can be expressed in the form:
\[ y = mx + c \]
where \( y \) is the dependent variable (volume), \( x \) is the independent variable (temperature), \( m \) is the slope, and \( c \) is the y-intercept.

### Step 3: Plotting the Graph
When we plot volume (V) on the y-axis and temperature (T) on the x-axis, according to Charles's Law, we will get a straight line that passes through the origin (0,0). This indicates that as the temperature increases, the volume also increases linearly.

### Step 4: Analyze the Options
Now, we need to analyze the options provided in the question to see which one corresponds to a volume versus temperature plot at constant pressure.

- If the option describes a graph of volume (V) against temperature (T), it will yield a linear plot.
- If any other option describes a different relationship (like pressure vs. volume or pressure vs. temperature), it will not yield a linear plot under constant pressure.

### Conclusion
The correct answer will be the option that represents the relationship between volume and temperature at constant pressure, which is consistent with Charles's Law.