Q: At what temperature does water reach its maximum density?

Water exhibits anomalous expansion between $0^\circ\text{C}$ and $4^\circ\text{C}$. As water is heated from $0^\circ\text{C}$ to $4^\circ\text{C}$, its volume decreases and density increases, reaching a maximum at $4^\circ\text{C}$. Hence, option A is correct.

Question 1

What is the SI unit of coefficient of thermal conductivity ($K$)?

Accepted Answer

The coefficient of thermal conductivity is defined as $K = \frac{Q \cdot d}{A \cdot \Delta T \cdot t}$. Substituting SI units: $\frac{	ext{J} \cdot 	ext{m}}{	ext{m}^2 \cdot 	ext{K} \cdot 	ext{s}} = 	ext{W m}^{-1} 	ext{K}^{-1}$. Hence, option A is correct.

Question 2

The ratio of coefficient of linear expansion ($\alpha$), area expansion ($\beta$), and volume expansion ($\gamma$) for an isotropic solid is:

Accepted Answer

For an isotropic solid, $\beta = 2\alpha$ and $\gamma = 3\alpha$. Therefore, $\alpha : \beta : \gamma = 1 : 2 : 3$. Hence, option A is correct.

Question 3

At what temperature do the Celsius and Fahrenheit scales read the exact same numerical value?

Accepted Answer

Using the relation $\frac{C}{5} = \frac{F - 32}{9}$, let $C = F = x$. Then $\frac{x}{5} = \frac{x - 32}{9} \implies 9x = 5x - 160 \implies 4x = -160 \implies x = -40^\circ$. Hence, option A is correct.

Question 4

At what temperature does water reach its maximum density?

Accepted Answer

Water exhibits anomalous expansion between $0^\circ	ext{C}$ and $4^\circ	ext{C}$. As water is heated from $0^\circ	ext{C}$ to $4^\circ	ext{C}$, its volume decreases and density increases, reaching a maximum at $4^\circ	ext{C}$. Hence, option A is correct.

Question 5

According to the Stefan-Boltzmann law, the total energy radiated per second per unit area by a perfect black body is directly proportional to:

Accepted Answer

According to Stefan-Boltzmann Law, $E = \sigma T^4$, where $E$ is emissive power, $T$ is absolute temperature, and $\sigma$ is Stefan's constant. Thus $E \propto T^4$. Hence, option A is correct.

Thermal Properties of Matter