To solve the question of which curve obtained at constant temperature and for a given mass of a gas is not a straight line, we will analyze the relationships between pressure (P), volume (V), and the ideal gas law.
### Step-by-Step Solution:
1. **Understand the Ideal Gas Law**:
The ideal gas equation is given by:
\[
PV = nRT
\]
where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles of gas, \( R \) is the universal gas constant, and \( T \) is the temperature.
2. **Given Conditions**:
We are told that the temperature is constant and we have a given mass of gas. This means that the number of moles \( n \) is constant, as it is determined by the mass of the gas divided by its molar mass.
3. **Rearranging the Equation**:
For a constant mass of gas at constant temperature, we can express the ideal gas law as:
\[
PV = K
\]
where \( K = nRT \) is a constant.
4. **Analyzing the Relationship**:
Rearranging gives:
\[
P = \frac{K}{V}
\]
This indicates that pressure and volume are inversely related.
5. **Graph of P vs V**:
When plotting \( P \) against \( V \), we get a hyperbolic curve, which is not a straight line. This is because as volume increases, pressure decreases, and vice versa.
6. **Other Relationships**:
- If we plot \( P \) against \( \frac{1}{V} \):
\[
P = K \cdot \frac{1}{V}
\]
This relationship is linear, and the graph will be a straight line passing through the origin.
- If we plot \( V \) against \( \frac{1}{P} \):
\[
V = K \cdot \frac{1}{P}
\]
This is also a linear relationship, resulting in a straight line through the origin.
- If we plot \( PV \) against \( P \):
Since \( PV = K \), this will also yield a straight line, but it will not pass through the origin (as \( K \) is a constant greater than zero).
7. **Conclusion**:
The only relationship that does not yield a straight line is the graph of \( P \) versus \( V \), which is a hyperbola. Therefore, the curve that is not a straight line is the one representing the relationship between pressure and volume at constant temperature and a given mass of gas.
### Final Answer:
The curve obtained at constant temperature and for a given mass of gas that is not a straight line is the graph of \( P \) versus \( V \).
