Question

The partition wall of negligible volume between two adjacent systems of same composition having volume \(V\), temperature \(T\), pressure \(P\) and density \(d\) of each system, is removed to make one system. What will be the respective parameters of the new system?

• A. \(2V,\;2T,\;2P,\;2d\)
• B. \(2V,\;2T,\;2P,\;d\)
• C. \(2V,\;T,\;2P,\;2d\)
• D. \(2V,\;T,\;P,\;d\)

Hint:

Extensive Properties: Mass, Volume, Internal Energy Intensive Properties: Temperature, Pressure, Density When identical systems are combined, extensive properties add up while intensive properties remain unchanged.

Answer 1

The Correct Option is D

Step 1: Picture the setup.
Two identical gas systems sit side by side. The thin wall between them is pulled out so the two combine into one bigger system.

Step 2: What happens to volume.
Volume is extensive, meaning it adds up. Two parts of volume $V$ each give a total of $V+V = 2V$.

Step 3: What happens to temperature.
Both parts were already at the same temperature $T$. Mixing two equally warm gases does not change how hot they are, so temperature stays $T$.

Step 4: What happens to pressure.
Each side already pushed with pressure $P$, and the gas is the same on both sides. After removing the wall nothing changes the push, so pressure stays $P$.

Step 5: What happens to density.
Mass doubles and volume doubles together, so $\dfrac{2m}{2V} = \dfrac{m}{V} = d$. Density stays $d$.

Step 6: Collect the new values.
So the combined system has $2V, T, P, d$, which is the last option.
\[ \boxed{2V,\ T,\ P,\ d} \]