In gas laws, the combined gas law relates which set of state variables in a single relationship?

Introduction / Context:
The behaviour of an ideal gas can be described by several gas laws, such as Boyle law, Charles law and Gay Lussac law. Each of these laws relates two variables while keeping the third constant. The combined gas law merges these individual relationships into one equation that links pressure, volume and temperature for a fixed amount of gas. This question asks which set of variables the combined gas law relates.

Given Data / Assumptions:
- We are dealing with an ideal gas and a fixed amount of gas (constant number of moles).
- Pressure is usually denoted by P, volume by V and temperature by T (in kelvin).
- Boyle law relates P and V at constant T, Charles law relates V and T at constant P, and Gay Lussac law relates P and T at constant V.
- The combined gas law collects these into a single equation.

Concept / Approach:
The combined gas law is often written as P1 V1 / T1 = P2 V2 / T2 for a fixed amount of gas changing from one state to another. This shows that the product of pressure and volume divided by temperature is constant for a given quantity of gas. Thus, the combined gas law simultaneously relates pressure, volume and temperature. It does not hold any of these three fixed; instead, it describes how a change in one affects the others when the amount of gas remains constant.

Step-by-Step Solution:
Step 1: Recall Boyle law: P is inversely proportional to V at constant T. Step 2: Recall Charles law: V is directly proportional to T at constant P. Step 3: Recall Gay Lussac law: P is directly proportional to T at constant V. Step 4: Combine these relationships to obtain P V / T = constant for a fixed amount of gas. Step 5: Express this as P1 V1 / T1 = P2 V2 / T2, showing that P, V and T are all linked. Step 6: Conclude that the combined gas law relates volume, temperature and pressure together.

Verification / Alternative check:
The ideal gas equation P V = n R T, where n is the number of moles and R is the gas constant, also links pressure, volume and temperature. For a fixed amount of gas, n and R are constant, so P V / T is constant. This is consistent with the combined gas law and again shows that P, V and T are all involved. Solving the ideal gas equation for any two variables requires knowledge of the third, reinforcing the idea that all three are interconnected.

Why Other Options Are Wrong:
Volume and temperature only: This describes Charles law, not the combined gas law.
Temperature and pressure only: This describes Gay Lussac law, not the combined law on its own.
Volume and pressure only: This describes Boyle law, which holds temperature constant, not the combined law.

Common Pitfalls:
A common error is to memorise individual gas laws without seeing how they fit together. Students sometimes think the combined gas law is just one more formula rather than a summary of the three basic laws. Remember that combined gas law is essentially the ideal gas equation rearranged for a fixed amount of gas and that it connects P, V and T in one expression.

Final Answer:
The combined gas law relates volume, temperature and pressure together for a fixed amount of gas.