Question

Which of the following is the correct statement for an ideal gas (constant =\( \textit{energy}\) )?
 

• A.

  

• B.

  

• C.

  

• D.

  

Hint:

For ideal gas law problems, isolate the variables to determine their relationship (e.g., $P \propto \frac{1}{V}$ at constant T).

Answer 1

The Correct Option is A

Using the ideal gas law $PV = nRT$:
- Option (1): At constant $n$ and $T$, $PV = \text{constant}$, so $P \propto \frac{1}{V}$. This is a hyperbolic relationship, but over a small range, it approximates a straight line with a negative slope. Correct.
- Option (2): A positive slope contradicts $P \propto \frac{1}{V}$. Incorrect.
- Option (3): At constant $V$ and $n$, $P \propto T$. Thus, P vs. $\frac{1}{T}$ has a negative slope, but this is less commonly emphasized compared to P vs. V.
- Option (4): At constant $P$ and $n$, $V \propto T$, so V vs. $\frac{1}{T}$ has a negative slope, not positive. Incorrect.
Option (1) is the most standard correct statement for ideal gases in this context.