Question

I've seen some problems where this was the case: a fixed amount of ideal gas underwent a reversible process where temperature varied while pressure and volume were both held constant. How could that be possible? For an ideal gas, PV=nRT so, if three variables are defined, then the remaining variable can only take a single value to satisfy the equation. It seems impossible to me that such process can exist, at least, with the constraints established.

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Answer 1

Under the ideal gas law, holding two variables constant out of pressure, volume, and temperature should fix the third; however, real gases may exhibit non-ideal behaviors that allow for small variations in these conditions, such as those described by the van der Waals equation.

Step-by-step explanation:

You are correct in noting that for an ideal gas described by the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature, holding two of these variables constant would typically fix the third. However, there is a special case known as an isothermal process where the temperature is constant, and thus the product of pressure and volume is a constant. In this case, an isothermal process can occur when heat is transferred to or from the gas to maintain a constant temperature, even as it expands or compresses.

In the scenario you're describing, with constant pressure and volume, while temperature changes, the situation indeed sounds impossible under the strict confines of the ideal gas law. Nevertheless, real gases can exhibit non-ideal behavior, and for very small changes in temperature, a process may appear to hold pressure and volume constant due to the gas's properties or the onset of a phase change.