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

Concept: Volume is an extensive property and depends on the amount of substance, whereas temperature, pressure and density are intensive properties and remain unchanged when identical systems are combined.

Step 1: Determine the new volume. When two identical systems are combined, \[\begin{aligned} V_{\text{new}}=V+V=2V \end{aligned}\]

Step 2: Determine the new temperature and pressure. Since both systems are initially at the same temperature and pressure, \[\begin{aligned} T_{\text{new}}=T \end{aligned}\] and \[\begin{aligned} P_{\text{new}}=P \end{aligned}\]

Step 3: Determine the new density. Density is \[\begin{aligned} d=\frac{m}{V} \end{aligned}\] After combining, \[\begin{aligned} d_{\text{new}} =\frac{2m}{2V} =d \end{aligned}\]

Step 4: Summarize the new parameters. \[ \begin{aligned} \text{Volume} &:\quad 2V \\ \text{Temperature} &:\quad T \\ \text{Pressure} &:\quad P \\ \text{Density} &:\quad d \end{aligned} \] \[\begin{aligned} \boxed{(2V,\;T,\;P,\;d)} \end{aligned}\] Hence, option \(\mathbf{(D)}\) is correct.