# Thermal Properties of Matter - Class 11 - Physics

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## Extra Questions - Thermal Properties of Matter | NCERT | Physics | Class 11

The figure shows a system of two concentric spheres of radii $r_1$ and $r_2$ are kept at temperature $T_1$ and $T_2$, respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to

Option 1): $\frac{r_{1}r_{2}}{(r_{2}-r_{1})}$

Option 2): $(r_{2}-r_{1})$

Option 3): $(r_{2}-r_{1})(r_{1}r_{2})$

Option 4): In $\left(\frac{r_{2}}{r_{1}}\right)$

The problem involves determining how the radial rate of heat transfer between two concentric spheres (inner radius $r_1$ and outer radius $r_2$, at temperatures $T_1$ and $T_2$ respectively) depends on their radii. The radial rate of heat flow $Q$ in the space between the spheres can be analyzed through the concept of thermal conduction. According to Fourier's law of heat conduction, the rate at which heat transfers through a material is proportional to the temperature gradient and inversely proportional to the distance over which the temperature changes.

Consider the path of conduction between the inner and outer sphere:

The temperature difference between the spheres is $(T_2 - T_1)$.

The radial distance between the inner and outer sphere is $(r_2 - r_1)$.

**Heat flow** through a spherical shell is also influenced by the **surface area** through which the heat flows. The surface area of a sphere increases with the square of its radius. So, as the radius increases from $r_1$ to $r_2$, the surface area increases and the heat flux adjusts accordingly. Simplifying the scenario for steady-state conditions, and keeping the temperature gradients and material properties constant, the radial rate of heat flow can be framed as:

$$ Q = k \cdot A \cdot \frac{\Delta T}{\Delta r} $$

Where:

$k$ is the thermal conductivity.

$A = 4\pi r^2$ is the surface area through which heat is flowing at radius $r$.

$\Delta T = T_2 - T_1$ is the temperature difference.

$\Delta r = r_2 - r_1$ is the radial thickness (distance between the spheres).

Upon evaluating how $A$ varies with the radius between $r_1$ and $r_2$, and recognizing that the term likely falls off with $\frac{1}{r}$ given spherical geometry, the dependency of $Q$ on $r_1$ and $r_2$ simplifies to a form that matches with option provided in the question:

$$ Q \propto \frac{r_1 r_2}{r_2 - r_1} $$

Therefore, suggesting that the heat flow between these two spheres is **proportional to $\frac{r_1 r_2}{r_2 - r_1}$.** Hence, **Option 1) is correct.**

Two metal cubes $A$ and $B$ of same size are arranged as shown in Figure. The extreme ends of the combination are maintained at the indicated temperatures. The arrangement is thermally insulated. The coefficients of thermal conductivity of $A$ and $B$ are $300W/(m \cdot ^\circ C)$ and $200W/(m \cdot ^\circ C)$, respectively. After steady state is reached, the temperature $t$ of the interface will be...

$45^\circ C$

$90^\circ C$

$30^\circ C$

$60^\circ C$

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Given S-T (entropy vs temperature) diagram is of a reversible cyclic process. Which of the following statements is/are correct?

A. Work done by the system in the whole cycle is $60 \mathrm{KJ}$.

B. Input heat to the system by any process is $90 \mathrm{KJ}$.

C. Heat given out by the system in process $B-C$ is $120 \mathrm{KJ}$.

D. Work done by the system in process $C-D$ is $-30 \mathrm{KJ}$.

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A diatomic gas is heated at constant pressure. What fraction of the heat energy is used to increase the internal energy?

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Why does volume change with a change in temperature?

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When pressure remains constant, find the temperature at which the volume of a gas at $0^{\circ} \mathrm{C}$ will double itself.

(A) $273^{\circ} \mathrm{C}$

(B) $0^{\circ} \mathrm{C}$

(C) $100^{\circ} \mathrm{C}$

(D) $546^{\circ} \mathrm{C}$

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In general, substances shrink on cooling and their volume decreases. This increases their:

A) boiling point

B) freezing point

C) heat capacity

D) density

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An insulator like wood and rubber has a very low resistance.

A) True

B) False