Questions: Which of the following graphs (A,B,C,D) correctly represents the relationship between the pressure and the volume of an ideal gas that is held at constant temperature?

Which of the following graphs (A,B,C,D) correctly represents the relationship between the pressure and the volume of an ideal gas that is held at constant temperature?
Transcript text: Which of the following graphs (A,B,C,D) correctly represents the relationship between the pressure and the volume of an ideal gas that is held at constant temperature?
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Solution

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Solution Steps

Step 1: Recall the ideal gas law

The ideal gas law states that PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

Step 2: Determine the relationship between pressure and volume at constant temperature

Since the temperature is constant, nRT is constant. Therefore, PV = constant, which implies that P is inversely proportional to V. This means as V increases, P decreases, and vice-versa. Mathematically, this can be represented as $P = \frac{constant}{V}$.

Step 3: Identify the correct graph

Graph B represents an inverse relationship between P and V, where P decreases as V increases, matching the relationship derived from the ideal gas law at constant temperature.

Final Answer: The correct graph is B.

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