Which of the following plots best depicts the relationship between pressure and volume for an ideal gas at constant temperature?

• A. A straight line with a positive slope (P vs. V)
• B. A horizontal line indicating constant pressure regardless of volume (P vs. V)
• C. A straight line with a negative slope passing through the origin (P vs. V)
• D. A hyperbolic curve showing that as volume increases, pressure decreases (P vs. V)

Answer: (D)

Verified step by step guidance

1. Recall the ideal gas law, which is given by the equation \(P V = n R T\), where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles, \(R\) is the gas constant, and \(T\) is the temperature.
2. Since the problem states that the temperature is constant, and assuming the amount of gas (\(n\)) is also constant, the product \(P V\) must remain constant.
3. This means that pressure and volume are inversely proportional to each other, which can be expressed as \(P = \frac{\text{constant}}{V}\).
4. Graphically, an inverse relationship between \(P\) and \(V\) is represented by a hyperbolic curve, where as volume increases, pressure decreases, and vice versa.
5. Therefore, the plot that best depicts this relationship is a hyperbolic curve, not a straight line or a horizontal line.