If a gas has the same temperature throughout, which of the following statements about its pressure and volume is true according to the ideal gas law?

• A. Pressure and volume both remain constant.
• B. Pressure and volume are directly proportional.
• C. Pressure and volume are independent of each other.
• D. Pressure and volume are inversely proportional.

Answer: (D)

Verified step by step guidance

1. Recall the ideal gas law, which is given by the equation \(P \times V = n \times R \times T\), where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles of gas, \(R\) is the ideal gas constant, and \(T\) is temperature.
2. Since the problem states that the temperature \(T\) is constant throughout, and assuming the amount of gas \(n\) is also constant, the product \(n \times R \times T\) becomes a constant value.
3. Rewrite the ideal gas law under these conditions as \(P \times V = \text{constant}\), which means that pressure and volume multiply to give a constant value.
4. From this relationship, if the volume \(V\) increases, the pressure \(P\) must decrease to keep the product constant, and vice versa. This means pressure and volume are inversely proportional.
5. Therefore, the correct interpretation according to the ideal gas law is that pressure and volume are inversely proportional when temperature is constant.