If heat energy is given to an ideal gas at constant pressure, then select the graph which best represents the variation of VT with temperature (T).

Options

A.
B.
C.
D.

Answer

To solve the problem of how the volume (V) of an ideal gas varies with temperature (T) when heat energy is added 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 \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles, \(R\) is the universal gas constant, and \(T\) is the temperature.

2. **Constant Pressure Condition**:
Since heat is added at constant pressure, we can denote this constant pressure as \(P\). Thus, we can rewrite the ideal gas law as:
\[ V = \frac{nRT}{P} \]
Here, \(n\) and \(R\) are constants, and \(P\) is also constant.

3. **Direct Proportionality**:
From the equation above, we can see that volume \(V\) is directly proportional to temperature \(T\):
\[ V \propto T \]
This means that as temperature increases, volume also increases.

4. **Expressing Volume in Terms of Temperature**:
We can express this relationship mathematically as:
\[ V = kT \]
where \(k = \frac{nR}{P}\) is a constant.

5. **Finding the Relationship Between VT and T**:
To find the relationship between \(VT\) and \(T\), we multiply both sides of the equation \(V = kT\) by \(T\):
\[ VT = kT^2 \]
This indicates that \(VT\) is proportional to \(T^2\).

6. **Identifying the Graph**:
The equation \(VT = kT^2\) represents a quadratic relationship, which is a parabola opening upwards. Therefore, the graph of \(VT\) versus \(T\) will be a curve that starts from the origin and increases as \(T\) increases.

### Conclusion:
The graph that best represents the variation of \(VT\) with temperature \(T\) is a parabola opening upwards.

---