Which of the following graphs best represents the relationship between pressure (P) and temperature (T) for a fixed volume of an ideal gas?

• A. A horizontal line, showing P is independent of T
• B. A straight line with a negative slope, showing P decreases as T increases
• C. A curve that increases exponentially as T increases
• D. A straight line passing through the origin, showing P increases linearly with T

Answer: (D)

Verified step by step guidance

1. Recall the ideal gas law, which relates pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T): \(P V = n R T\).
2. Since the volume (V) and the amount of gas (n) are fixed, and R is a constant, we can rearrange the equation to express pressure as a function of temperature: \(P = \frac{n R}{V} T\).
3. Notice that \(\frac{n R}{V}\) is a constant, so pressure (P) is directly proportional to temperature (T). This means if you plot P versus T, the graph will be a straight line.
4. Because pressure is zero when temperature is zero (in Kelvin), the line passes through the origin (0,0).
5. Therefore, the graph that best represents the relationship between pressure and temperature at constant volume is a straight line passing through the origin, showing that pressure increases linearly with temperature.