IMO Practice Test: Thermal Properties of Matter | Class 11 Physics

Question 1 of 12

Two rods of the same material and length but cross-sections in the ratio 1:2 carry heat between the same two reservoirs. The ratio of their rates of heat flow is:

$1:1$

$1:2$

$2:1$

$1:4$

Explanation: $\frac{Q}{t}\propto A$, so the ratio of rates equals the ratio of areas, $1:2$.

Question 2 of 12

A metal ring is heated. The diameter of its central hole will:

decrease

increase

stay the same

first decrease then increase

Explanation: On heating, every dimension scales up, so the hole expands just like the metal — its diameter increases.

Question 3 of 12

Equal masses of ice at $0\,^\circ$C and water at $80\,^\circ$C are mixed. ($L_f=80\ \text{cal/g}$, $c_w=1\ \text{cal/g}\,^\circ$C.) The final state is:

all ice at $0\,^\circ$C

all water at $0\,^\circ$C

ice-water mixture at $0\,^\circ$C

all water at $40\,^\circ$C

Explanation: Heat from water $=m\times1\times80=80m$ cal; to melt the ice needs $80m$ cal. Exactly enough, so all becomes water at $0\,^\circ$C.

Question 4 of 12

A rod is rigidly clamped at both ends and heated through $\Delta T$. The thermal strain produced is:

$\alpha\,\Delta T$

$\frac{\alpha}{\Delta T}$

$\alpha^2\,\Delta T$

zero

Explanation: Prevented expansion gives a compressive strain equal to the free fractional expansion, $\frac{\Delta L}{L}=\alpha\,\Delta T$.

Question 5 of 12

If the absolute temperature of a black body is increased by 10%, the energy radiated per unit area increases by about:

10%

21%

40%

46%

Explanation: $E\propto T^4$; $(1.1)^4\approx1.464$, an increase of about 46%.

Question 6 of 12

Two bodies of the same material and same surface finish have radii in the ratio 1:2 at the same temperature. The ratio of their rates of energy radiation is:

$1:2$

$1:4$

$1:8$

$1:16$

Explanation: Radiated power $P=e\sigma A T^4\propto A\propto r^2$; $(1:2)^2=1:4$.

Question 7 of 12

Two rods of conductivities $k_1$ and $k_2$, equal length and area, are joined end to end. The effective conductivity of the combination is:

$k_1+k_2$

$\frac{k_1+k_2}{2}$

$\frac{2k_1k_2}{k_1+k_2}$

$\sqrt{k_1k_2}$

Explanation: For series (end to end), thermal resistances add, giving the harmonic-type result $k_{eff}=\frac{2k_1k_2}{k_1+k_2}$.

Question 8 of 12

A liquid cools from $70\,^\circ$C to $60\,^\circ$C in 5 min and from $60\,^\circ$C to $50\,^\circ$C in 8 min, in surroundings at temperature $T_s$. This shows that cooling:

speeds up over time

slows down over time

is constant

stops

Explanation: The second 10 degrees take longer because the temperature excess over the surroundings is smaller (Newton's law of cooling).

Question 9 of 12

A solid sphere and a hollow sphere of the same material, mass and surface finish at the same temperature radiate. Initially they radiate energy:

equally per second

the hollow one faster

the solid one faster

neither radiates

Explanation: For equal mass, the hollow sphere has a larger surface area, so by $P\propto A$ it radiates faster initially.

Question 10 of 12

The wavelength of maximum emission of a star is half that of the Sun. The star's surface temperature compared with the Sun's is:

half

the same

twice

four times

Explanation: By Wien's law $\lambda_m T=$ constant; halving $\lambda_m$ doubles $T$.

Question 11 of 12

5 g of steam at $100\,^\circ$C is passed into 100 g of water at $20\,^\circ$C. ($L_v=540\ \text{cal/g}$, $c_w=1$.) The heat released by the condensing steam alone is:

$540\ \text{cal}$

$2700\ \text{cal}$

$5400\ \text{cal}$

$100\ \text{cal}$

Explanation: Condensation releases $mL_v=5\times540=2700\ \text{cal}$ before the condensed water even begins to cool.

Question 12 of 12

A bimetallic strip bends on heating because the two metals have different:

densities

specific heats

coefficients of linear expansion

melting points

Explanation: Unequal values of $\alpha$ make one metal expand more than the other, so the strip curves towards the metal with the smaller $\alpha$.

IMO Practice Test — Thermal Properties of Matter