Which of the following is a correct plot of the volume of fixed amount of ideal gas as a function of temperature (at constant pressure)

Options

A.
B.
C.
D.

Answer

To solve the question regarding the correct plot of the volume of a fixed amount of ideal gas as a function of temperature at constant pressure, we can follow these steps:

### Step-by-Step Solution:

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
- \( R \) = Ideal gas constant
- \( T \) = Temperature in Kelvin

2. **Identify Constants**: In this scenario, we are keeping pressure \( P \), the number of moles \( n \), and the gas constant \( R \) constant. Therefore, the equation can be simplified to relate volume and temperature:
\[ V \propto T \]
This indicates that volume \( V \) is directly proportional to temperature \( T \).

3. **Formulate the Relationship**: To express this relationship mathematically, we can write:
\[ V = kT \]
where \( k \) is a constant of proportionality.

4. **Graphing the Relationship**: When we plot volume \( V \) against temperature \( T \) (in Kelvin), the graph will be a straight line passing through the origin (0,0). This is because when \( T = 0 \), \( V \) also equals 0, indicating a linear relationship.

5. **Consider Temperature in Celsius**: If we consider temperature in degrees Celsius instead of Kelvin, we need to convert it:
\[ T(°C) = T(K) - 273.15 \]
This means the relationship becomes:
\[ V = k(T(°C) + 273.15) \]
This indicates that the graph will still be linear but will have a y-intercept at \( 273.15 \) when plotted against temperature in Celsius.

6. **Evaluate the Options**:
- If the plot is of volume \( V \) vs. temperature \( T \) in Kelvin, it will be a straight line through the origin.
- If the plot is of volume \( V \) vs. temperature in degrees Celsius, it will be a straight line with a positive y-intercept at \( 273.15 \).
- Any plot showing a negative slope or a curve is incorrect.

7. **Conclusion**: Based on the analysis, the correct plot is the one that shows a straight line for volume versus temperature in Kelvin (Option 3).