Which of the following graphs relates V and T?

Options

A.
B.
C.
D.

Explanation

To solve the question of which graph relates volume (V) and temperature (T) according to Charles' Law, we can follow these steps:

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

### Step 2: Identify the Relationship
Since volume is directly proportional to temperature, if the temperature increases, the volume will also increase, and vice versa. This indicates a linear relationship between V and T.

### Step 3: Analyze the Graph Options
1. **Option 1**: A straight line passing through the origin. This represents a direct proportionality, which aligns with Charles' Law.
2. **Option 2**: A hyperbolic curve. This indicates an inverse relationship, which does not apply here.
3. **Option 3**: A horizontal line. This suggests that volume does not change with temperature, which contradicts Charles' Law.
4. **Option 4**: A straight line that does not pass through the origin. This would imply a non-zero intercept, indicating that volume does not start from zero when temperature is zero, which is incorrect for an ideal gas.

### Step 4: Conclusion
Based on the analysis, **Option 1** is the correct graph that relates volume (V) and temperature (T) according to Charles' Law.

### Final Answer
The correct graph that relates V and T is **Option 1**.

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