Question

Which of the following graphs is correctly drawn between temperature \((t)\) and density \((d)\) of water?

• A. Graph 1
• B. Graph 2
• C. Graph 3
• D. Graph 4

Hint:

A very important fact: \[ \boxed{\text{Density of water is maximum at }4^\circ\text{C}} \] and \[ \boxed{\text{Volume of water is minimum at }4^\circ\text{C}}. \] This is called the anomalous expansion of water.

Answer 1

The Correct Option is B

Concept: Water exhibits

anomalous expansion between \[ 0^\circ\text{C} \quad \text{and} \quad 4^\circ\text{C}. \] Its density increases as temperature rises from \(0^\circ\text{C}\) to \(4^\circ\text{C}\), and beyond \(4^\circ\text{C}\) the density decreases.

Step 1: Recall the variation of density of water with temperature. At \[ 0^\circ\text{C}, \] water has density approximately \[ 1.000\ \text{g cm}^{-3}. \] As temperature increases to \[ 4^\circ\text{C}, \] the density increases and becomes maximum: \[ \rho_{\max} = 1.000\ \text{g cm}^{-3} \ (\text{approximately }1.000\text{ or }1.001). \]

Step 2: Behaviour beyond \(4^\circ\text{C}\). For \[ T\gt 4^\circ\text{C}, \] water expands normally, so its density decreases with increase in temperature. Thus the density-temperature graph must: \[ \text{increase from }0^\circ\text{C}\text{ to }4^\circ\text{C}, \] reach a maximum at \[ 4^\circ\text{C}, \] and then decrease.

Step 3: Identify the correct graph. Among the given graphs, only Graph 2 shows: \[ \text{Maximum density at }4^\circ\text{C}. \] Hence it correctly represents the anomalous behaviour of water. Therefore, \[ \boxed{\text{Graph 2 is correct}} \] \[ \boxed{\text{Answer = (B)}} \]