Question

The ratio of any two extensive properties is independent of:

• A. Total mass
• B. Total heat
• C. Total system
• D. Total time

Hint:

Ratio of two extensive properties always becomes an intensive property.

Answer 1

The Correct Option is C

Concept: Extensive properties are those which depend on the size or extent of the system, such as mass, volume, internal energy, entropy, etc. If two extensive properties are considered: \[ X \propto \text{system size}, \quad Y \propto \text{system size} \] then their ratio becomes: \[ \frac{X}{Y} = \text{independent of system size} \] This is because scaling the system scales both numerator and denominator equally.

Step 1: Understand scaling behavior.
If system is doubled: \[ X \rightarrow 2X, \quad Y \rightarrow 2Y \] So: \[ \frac{2X}{2Y} = \frac{X}{Y} \] Hence ratio is independent of system extent.

Step 2: Interpret options.
- Mass affects extensive properties → not correct - Heat is not a state property → irrelevant - System size affects extensives → correct independence - Time is unrelated Final Answer: \[ \boxed{\text{Independent of total system}} \]