Grade 11 : Physics - Thermal Properties (Set 3)

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Grade 11 : Physics - Thermal Properties (Set 3)— Questions & Detailed Solutions

A steel rod of Young's modulus $Y = 2 \times 10^{11}\text{ N/m}^2$ and coefficient of linear expansion $\alpha = 1.2 \times 10^{-5}\text{ K}^{-1}$ is clamped rigidly between two fixed vertical walls.
If the temperature of the rod is increased by $50^\circ\text{C}$, what is the thermal stress developed inside the rod?

(A)

60 MPa

(B)

120 MPa

(C)

180 MPa

(D)

240 MPa

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation:Thermal stress is given by $\sigma = Y \alpha \Delta T$. Substituting the values: $\sigma = (2 \times 10^{11}) \times (1.2 \times 10^{-5}) \times 50 = 1.2 \times 10^8\text{ N/m}^2 = 120\text{ MPa}$.

In a calorimetry experiment, 40 g of ice at $0^\circ\text{C}$ is mixed with 40 g of liquid water at $40^\circ\text{C}$ in an insulated vessel.
Given latent heat of fusion $L_f = 80\text{ cal/g}$ and specific heat of water $c = 1\text{ cal/g}^\circ\text{C}$, what is the final state of the mixture?

(A)

$0^\circ\text{C}$ with 20 g ice remaining

(B)

$0^\circ\text{C}$ with 0 g ice remaining

(C)

$5^\circ\text{C}$ all liquid water

(D)

$10^\circ\text{C}$ all liquid water

View Correct Answer & Detailed Solution

✓ Correct Option: (A)

Explanation:Heat required to melt all ice $= 40 \times 80 = 3200\text{ cal}$. Heat available from cooling water to $0^\circ\text{C} = 40 \times 1 \times 40 = 1600\text{ cal}$. Mass of ice melted $= 1600 / 80 = 20g$. Hence, the final temperature is $0^\circ\text{C}$ with $40 - 20 = 20g$ of ice remaining.

A composite slab consists of two layers of equal thickness $d$ placed end to end with thermal conductivities $K_1 = 100\text{ W/m}\cdot\text{K}$ and $K_2 = 300\text{ W/m}\cdot\text{K}$.
What is the effective thermal conductivity $K_{eq}$ of the composite slab for series heat flow?

(A)

$150\text{ W/m}\cdot\text{K}$

(B)

$200\text{ W/m}\cdot\text{K}$

(C)

$225\text{ W/m}\cdot\text{K}$

(D)

$250\text{ W/m}\cdot\text{K}$

View Correct Answer & Detailed Solution

✓ Correct Option: (A)

Explanation:For two layers of equal thickness in series, $K_{eq} = \frac{2 K_1 K_2}{K_1 + K_2}$. $K_{eq} = \frac{2 \times 100 \times 300}{100 + 300} = \frac{60000}{400} = 150\text{ W/m}\cdot\text{K}$.

According to Newton's law of cooling, a body cools from $80^\circ\text{C}$ to $60^\circ\text{C}$ in 5 minutes when the surrounding temperature is $20^\circ\text{C}$.
Assuming linear approximation, how long will it take for the body to cool from $60^\circ\text{C}$ to $40^\circ\text{C}$ under the same conditions?

(A)

5.0 min

(B)

6.5 min

(C)

8.33 min

(D)

10.0 min

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation:Case 1: $\frac{80-60}{5} = K(70 - 20) \Rightarrow 4 = 50K \Rightarrow K = 0.08\text{ min}^{-1}$. Case 2: $\frac{60-40}{t} = K(50 - 20) \Rightarrow \frac{20}{t} = 0.08 \times 30 = 2.4 \Rightarrow t = \frac{20}{2.4} = 8.33\text{ min}$.

A solid copper sphere of radius $R$ at absolute temperature $T$ radiates thermal power $P$. If the radius of the sphere is doubled to $2R$ and its absolute temperature is doubled to $2T$, what is the new total radiated power $P'$?

(A)

$8P$

(B)

$16P$

(C)

$32P$

(D)

$64P$

View Correct Answer & Detailed Solution

✓ Correct Option: (D)

Explanation:By Stefan-Boltzmann law, $P = \sigma A T^4 = \sigma (4\pi R^2) T^4 \propto R^2 T^4$. Thus, $P' \propto (2R)^2 (2T)^4 = 4 R^2 \times 16 T^4 = 64 P$.

The wavelength of maximum radiation intensity emitted by a black body at temperature 2000 K is $\lambda_1 = 1.5\ \mum$. What will be the peak wavelength $\lambda_2$ if the temperature is raised to 3000 K?

(A)

$0.75\ \mum$

(B)

$1.0\ \mum$

(C)

$1.25\ \mum$

(D)

$2.25\ \mum$

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation:By Wien's displacement law, $\lambda_m T = \text{constant}$. $\lambda_1 T_1 = \lambda_2 T_2 \Rightarrow 1.5 \times 2000 = \lambda_2 \times 3000 \Rightarrow \lambda_2 = 1.0\ \mum$.

A pendulum clock with a brass rod ($\alpha = 2 \times 10^{-5}\text{ K}^{-1}$) keeps accurate time at $20^\circ\text{C}$.
If the ambient temperature increases to $30^\circ\text{C}$, how much time does the clock lose or gain per day?

(A)

Gains 8.64 s

(B)

Loses 8.64 s

(C)

Loses 4.32 s

(D)

Gains 4.32 s

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation:Time loss per day is $\Delta t = \frac{1}{2} \alpha \Delta \theta \times 86400\text{ s} = \frac{1}{2} \times (2 \times 10^{-5}) \times 10 \times 86400 = 8.64\text{ s}$. Since length increases, time period increases, so the clock loses time.

A glass flask ($\alpha_{glass} = 1 \times 10^{-5}\text{ K}^{-1}$) of volume $1000cm^3$ is completely filled with liquid at $20^\circ\text{C}$. The real cubical expansion coefficient of the liquid is $\gamma_r = 6 \times 10^{-4}\text{ K}^{-1}$. What volume of liquid overflows when heated to $70^\circ\text{C}$?

(A)

$15.0cm^3$

(B)

$28.5cm^3$

(C)

$30.0cm^3$

(D)

$33.5cm^3$

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation:$\gamma_{glass} = 3 \alpha_{glass} = 3 \times 10^{-5}\text{ K}^{-1} = 0.3 \times 10^{-4}\text{ K}^{-1}$. Apparent expansion coefficient $\gamma_{app} = \gamma_r - \gamma_{glass} = 5.7 \times 10^{-4}\text{ K}^{-1}$. Overflow $\Delta V_{app} = V_0 \gamma_{app} \Delta T = 1000 \times 5.7 \times 10^{-4} \times 50 = 28.5cm^3$.

A faulty thermometer has its lower fixed point at $5^\circ\text{C}$ and upper fixed point at $95^\circ\text{C}$. When this thermometer reads $41^\circ\text{C}$, what is the correct reading on the standard Celsius scale?

(A)

$35^\circ\text{C}$

(B)

$40^\circ\text{C}$

(C)

$45^\circ\text{C}$

(D)

$48^\circ\text{C}$

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation:Using scale formula: $\frac{X - LFP}{UFP - LFP} = \frac{C - 0}{100 - 0}$. $\frac{41 - 5}{95 - 5} = \frac{36}{90} = 0.4 = \frac{C}{100} \Rightarrow C = 40^\circ\text{C}$.

Q10

On a frozen lake surface, an ice sheet of thickness 2 cm forms in 10 minutes when atmospheric temperature is $-10^\circ\text{C}$.
How much additional time is required for the ice layer to grow from a thickness of 2 cm to 4 cm?

(A)

10 min

(B)

20 min

(C)

30 min

(D)

40 min

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation:Time taken for ice growth $t \propto (x_2^2 - x_1^2)$. For $0 \to 2cm$: $t_1 \propto (2^2 - 0^2) = 4$. For $2 \to 4cm$: $t_2 \propto (4^2 - 2^2) = 12$. $\frac{t_2}{t_1} = \frac{12}{4} = 3 \Rightarrow t_2 = 3 \times 10 = 30\text{ min}$.

Q11

Two cylindrical rods of the same metal have lengths in ratio $1:2$ and radii in ratio $2:1$. If they are connected in parallel across identical temperature differences, what is the ratio of heat current through rod 1 to rod 2 ($H_1 / H_2$)?

(A)

$1 : 8$

(B)

$2 : 1$

(C)

$4 : 1$

(D)

$8 : 1$

View Correct Answer & Detailed Solution

✓ Correct Option: (D)

Explanation:Thermal resistance $R = \frac{L}{K A} = \frac{L}{K \pi r^2}$. $\frac{R_1}{R_2} = \frac{L_1}{L_2} \times \left(\frac{r_2}{r_1}\right)^2 = \frac{1}{2} \times \left(\frac{1}{2}\right)^2 = \frac{1}{8}$. Heat current $H = \frac{\Delta T}{R} \Rightarrow \frac{H_1}{H_2} = \frac{R_2}{R_1} = 8 : 1$.

Q12

A copper block of mass 0.84 kg at $100^\circ\text{C}$ is placed into a large cavity in an ice block at $0^\circ\text{C}$. If specific heat of copper is $400\text{ J/kg}\cdot\text{K}$ and latent heat of fusion of ice is $3.36 \times 10^5\text{ J/kg}$, what mass of ice melts?

(A)

50 g

(B)

100 g

(C)

150 g

(D)

200 g

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation:Heat lost by copper block $Q = m c \Delta T = 0.84 \times 400 \times 100 = 33600\text{ J}$. Mass of ice melted $m_{ice} = \frac{Q}{L_f} = \frac{33600}{3.36 \times 10^5} = 0.1kg = 100g$.

Q13

A body radiates energy at rate $P$ in vacuum at temperature 300 K. If its absolute temperature is tripled to 900 K, what is the new rate of energy radiation according to Stefan-Boltzmann law?

(A)

$9P$

(B)

$27P$

(C)

$81P$

(D)

$243P$

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation:Radiated power $P \propto T^4$. Thus, $\frac{P'}{P} = \left(\frac{900}{300}\right)^4 = 3^4 = 81 \Rightarrow P' = 81P$.

Q14

A copper calorimeter of mass 100 g ($c_{Cu} = 0.1\text{ cal/g}^\circ\text{C}$) contains 140 g of water at $15^\circ\text{C}$.
If 50 g of water at $55^\circ\text{C}$ is added to the calorimeter, what is the final thermal equilibrium temperature?

(A)

$20^\circ\text{C}$

(B)

$25^\circ\text{C}$

(C)

$30^\circ\text{C}$

(D)

$35^\circ\text{C}$

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation:Water equivalent of calorimeter $W = 100 \times 0.1 = 10g$. Total cold water equivalent $= 140 + 10 = 150g$. Heat lost $=$ Heat gained: $50 \times (55 - T_f) = 150 \times (T_f - 15) \Rightarrow 55 - T_f = 3T_f - 45 \Rightarrow 4T_f = 100 \Rightarrow T_f = 25^\circ\text{C}$.

Q15

A hollow spherical shell made of aluminum has inner radius $r_1$ and outer radius $r_2$. When the entire shell is heated uniformly, what happens to $r_1$ and $r_2$?

(A)

$r_1$ increases and $r_2$ decreases

(B)

$r_1$ decreases and $r_2$ increases

(C)

Both $r_1$ and $r_2$ increase proportionally

(D)

$r_1$ remains constant while $r_2$ increases

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation:Thermal expansion acts like a photographic enlargement. Every linear dimension of a body increases upon heating, including internal cavities. Therefore, both $r_1$ and $r_2$ increase proportionally.

Q16

A conducting rod of length $L$ and cross-sectional area $A$ has position-dependent thermal conductivity $K(x) = K_0 (1 + x/L)$ along its length.
If the ends at $x=0$ and $x=L$ are maintained at steady temperatures $T_1$ and $T_2$ ($T_1 > T_2$), what is the steady-state rate of heat flow $H$?

(A)

$\frac{K_0 A (T_1 - T_2)}{L \ln 2}$

(B)

$\frac{K_0 A (T_1 - T_2)}{L} \ln 2$

(C)

$\frac{2 K_0 A (T_1 - T_2)}{L}$

(D)

$\frac{K_0 A (T_1 - T_2)}{2L}$

View Correct Answer & Detailed Solution

✓ Correct Option: (A)

Explanation:Heat current $H = -K(x) A \frac{dT}{dx}$. Rearranging gives $\frac{H}{K_0 A} \int_0^L \frac{dx}{1 + x/L} = -\int_{T_1}^{T_2} dT = T_1 - T_2$. Integrating: $\frac{H L}{K_0 A} \ln 2 = T_1 - T_2 \Rightarrow H = \frac{K_0 A (T_1 - T_2)}{L \ln 2}$.

Q17

The average solar radiant energy reaching Earth's surface per unit area per unit time is the solar constant $S$. If the mean distance between Earth and Sun were halved, what would be the new solar constant $S'$?

(A)

$S/4$

(B)

$S/2$

(C)

$2S$

(D)

$4S$

View Correct Answer & Detailed Solution

✓ Correct Option: (D)

Explanation:Solar constant follows inverse square law: $S = \frac{P_{sun}}{4 \pi r^2} \propto \frac{1}{r^2}$. If $r' = r/2$, $S' \propto \frac{1}{(r/2)^2} = 4S$.

Q18

A bimetallic strip of total thickness $d$ consists of two thin metal strips of equal thickness bonded together, with linear expansion coefficients $\alpha_1$ and $\alpha_2$ (where $\alpha_1 > \alpha_2$).
When heated by temperature difference $\Delta T$, the strip bends into a circular arc. What is the radius of curvature $R$ of the strip?

(A)

$R \approx \frac{d}{(\alpha_1 - \alpha_2) \Delta T}$

(B)

$R \approx \frac{d (\alpha_1 - \alpha_2)}{\Delta T}$

(C)

$R \approx \frac{2d}{(\alpha_1 + \alpha_2) \Delta T}$

(D)

$R \approx \frac{d}{\alpha_1 \alpha_2 \Delta T}$

View Correct Answer & Detailed Solution

✓ Correct Option: (A)

Explanation:For a bimetallic strip of two equal layers of thickness $d/2$, difference in length $\frac{\Delta L}{L} = (\alpha_1 - \alpha_2) \Delta T = \frac{d}{R}$. Thus, radius of curvature $R \approx \frac{d}{(\alpha_1 - \alpha_2) \Delta T}$.

Q19

Dry steam at $100^\circ\text{C}$ is passed into 500 g of liquid water at $20^\circ\text{C}$ inside a calorimeter of negligible heat capacity.
Given $L_v = 540\text{ cal/g}$ and $c_w = 1\text{ cal/g}^\circ\text{C}$, what is the final mass of liquid water in the container at equilibrium?

(A)

500 g

(B)

574 g

(C)

600 g

(D)

426 g

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation:Heat needed to raise water to $100^\circ\text{C} = 500 \times 1 \times 80 = 40000\text{ cal}$. Mass of steam required to condense $m = \frac{40000}{540} \approx 74.07g$. Total liquid water at $100^\circ\text{C} = 500 + 74.07 = 574.07g \approx 574g$.

Q20

Prevost's Theory of Heat Exchange:
Statement I: All bodies above absolute zero emit thermal radiation continuously.
Statement II: A body in thermal equilibrium with its surroundings ceases radiation exchange.
Which statement correctly describes a body in thermal equilibrium with its surroundings?

(A)

It stops emitting thermal radiation completely

(B)

It emits and absorbs thermal radiation at equal rates

(C)

It only absorbs radiation without emitting any

(D)

Its emissivity becomes exactly equal to zero

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation:According to Prevost's theory, every body continuously emits thermal radiation at a rate depending only on its temperature and surface properties. At thermal equilibrium, the rate of emission equals the rate of absorption.

Grade 11 : Physics - Thermal Properties (Set 3)

Grade 11 : Physics - Thermal Properties (Set 3)— Questions & Detailed Solutions

In a calorimetry experiment, 40 g of ice at $0^\circ\text{C}$ is mixed with 40 g of liquid water at $40^\circ\text{C}$ in an insulated vessel.
Given latent heat of fusion $L_f = 80\text{ cal/g}$ and specific heat of water $c = 1\text{ cal/g}^\circ\text{C}$, what is the final state of the mixture?

A composite slab consists of two layers of equal thickness $d$ placed end to end with thermal conductivities $K_1 = 100\text{ W/m}\cdot\text{K}$ and $K_2 = 300\text{ W/m}\cdot\text{K}$.
What is the effective thermal conductivity $K_{eq}$ of the composite slab for series heat flow?

A solid copper sphere of radius $R$ at absolute temperature $T$ radiates thermal power $P$. If the radius of the sphere is doubled to $2R$ and its absolute temperature is doubled to $2T$, what is the new total radiated power $P'$?

The wavelength of maximum radiation intensity emitted by a black body at temperature 2000 K is $\lambda_1 = 1.5\ \mum$. What will be the peak wavelength $\lambda_2$ if the temperature is raised to 3000 K?

A pendulum clock with a brass rod ($\alpha = 2 \times 10^{-5}\text{ K}^{-1}$) keeps accurate time at $20^\circ\text{C}$.
If the ambient temperature increases to $30^\circ\text{C}$, how much time does the clock lose or gain per day?

A faulty thermometer has its lower fixed point at $5^\circ\text{C}$ and upper fixed point at $95^\circ\text{C}$. When this thermometer reads $41^\circ\text{C}$, what is the correct reading on the standard Celsius scale?

On a frozen lake surface, an ice sheet of thickness 2 cm forms in 10 minutes when atmospheric temperature is $-10^\circ\text{C}$.
How much additional time is required for the ice layer to grow from a thickness of 2 cm to 4 cm?

Two cylindrical rods of the same metal have lengths in ratio $1:2$ and radii in ratio $2:1$. If they are connected in parallel across identical temperature differences, what is the ratio of heat current through rod 1 to rod 2 ($H_1 / H_2$)?

A copper block of mass 0.84 kg at $100^\circ\text{C}$ is placed into a large cavity in an ice block at $0^\circ\text{C}$. If specific heat of copper is $400\text{ J/kg}\cdot\text{K}$ and latent heat of fusion of ice is $3.36 \times 10^5\text{ J/kg}$, what mass of ice melts?

A body radiates energy at rate $P$ in vacuum at temperature 300 K. If its absolute temperature is tripled to 900 K, what is the new rate of energy radiation according to Stefan-Boltzmann law?

A copper calorimeter of mass 100 g ($c_{Cu} = 0.1\text{ cal/g}^\circ\text{C}$) contains 140 g of water at $15^\circ\text{C}$.
If 50 g of water at $55^\circ\text{C}$ is added to the calorimeter, what is the final thermal equilibrium temperature?

A hollow spherical shell made of aluminum has inner radius $r_1$ and outer radius $r_2$. When the entire shell is heated uniformly, what happens to $r_1$ and $r_2$?

A conducting rod of length $L$ and cross-sectional area $A$ has position-dependent thermal conductivity $K(x) = K_0 (1 + x/L)$ along its length.
If the ends at $x=0$ and $x=L$ are maintained at steady temperatures $T_1$ and $T_2$ ($T_1 > T_2$), what is the steady-state rate of heat flow $H$?

The average solar radiant energy reaching Earth's surface per unit area per unit time is the solar constant $S$. If the mean distance between Earth and Sun were halved, what would be the new solar constant $S'$?

Dry steam at $100^\circ\text{C}$ is passed into 500 g of liquid water at $20^\circ\text{C}$ inside a calorimeter of negligible heat capacity.
Given $L_v = 540\text{ cal/g}$ and $c_w = 1\text{ cal/g}^\circ\text{C}$, what is the final mass of liquid water in the container at equilibrium?

Prevost's Theory of Heat Exchange:
Statement I: All bodies above absolute zero emit thermal radiation continuously.
Statement II: A body in thermal equilibrium with its surroundings ceases radiation exchange.
Which statement correctly describes a body in thermal equilibrium with its surroundings?

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Grade 11 : Physics - Thermal Properties (Set 3)

Grade 11 : Physics - Thermal Properties (Set 3)— Questions & Detailed Solutions

In a calorimetry experiment, 40 g of ice at $0^\circ\text{C}$ is mixed with 40 g of liquid water at $40^\circ\text{C}$ in an insulated vessel.Given latent heat of fusion $L_f = 80\text{ cal/g}$ and specific heat of water $c = 1\text{ cal/g}^\circ\text{C}$, what is the final state of the mixture?

A composite slab consists of two layers of equal thickness $d$ placed end to end with thermal conductivities $K_1 = 100\text{ W/m}\cdot\text{K}$ and $K_2 = 300\text{ W/m}\cdot\text{K}$.What is the effective thermal conductivity $K_{eq}$ of the composite slab for series heat flow?

A solid copper sphere of radius $R$ at absolute temperature $T$ radiates thermal power $P$. If the radius of the sphere is doubled to $2R$ and its absolute temperature is doubled to $2T$, what is the new total radiated power $P'$?

The wavelength of maximum radiation intensity emitted by a black body at temperature 2000 K is $\lambda_1 = 1.5\ \mum$. What will be the peak wavelength $\lambda_2$ if the temperature is raised to 3000 K?

A pendulum clock with a brass rod ($\alpha = 2 \times 10^{-5}\text{ K}^{-1}$) keeps accurate time at $20^\circ\text{C}$.If the ambient temperature increases to $30^\circ\text{C}$, how much time does the clock lose or gain per day?

A faulty thermometer has its lower fixed point at $5^\circ\text{C}$ and upper fixed point at $95^\circ\text{C}$. When this thermometer reads $41^\circ\text{C}$, what is the correct reading on the standard Celsius scale?

On a frozen lake surface, an ice sheet of thickness 2 cm forms in 10 minutes when atmospheric temperature is $-10^\circ\text{C}$.How much additional time is required for the ice layer to grow from a thickness of 2 cm to 4 cm?

Two cylindrical rods of the same metal have lengths in ratio $1:2$ and radii in ratio $2:1$. If they are connected in parallel across identical temperature differences, what is the ratio of heat current through rod 1 to rod 2 ($H_1 / H_2$)?

A copper block of mass 0.84 kg at $100^\circ\text{C}$ is placed into a large cavity in an ice block at $0^\circ\text{C}$. If specific heat of copper is $400\text{ J/kg}\cdot\text{K}$ and latent heat of fusion of ice is $3.36 \times 10^5\text{ J/kg}$, what mass of ice melts?

A body radiates energy at rate $P$ in vacuum at temperature 300 K. If its absolute temperature is tripled to 900 K, what is the new rate of energy radiation according to Stefan-Boltzmann law?

A copper calorimeter of mass 100 g ($c_{Cu} = 0.1\text{ cal/g}^\circ\text{C}$) contains 140 g of water at $15^\circ\text{C}$.If 50 g of water at $55^\circ\text{C}$ is added to the calorimeter, what is the final thermal equilibrium temperature?

A hollow spherical shell made of aluminum has inner radius $r_1$ and outer radius $r_2$. When the entire shell is heated uniformly, what happens to $r_1$ and $r_2$?

A conducting rod of length $L$ and cross-sectional area $A$ has position-dependent thermal conductivity $K(x) = K_0 (1 + x/L)$ along its length.If the ends at $x=0$ and $x=L$ are maintained at steady temperatures $T_1$ and $T_2$ ($T_1 > T_2$), what is the steady-state rate of heat flow $H$?

The average solar radiant energy reaching Earth's surface per unit area per unit time is the solar constant $S$. If the mean distance between Earth and Sun were halved, what would be the new solar constant $S'$?

Dry steam at $100^\circ\text{C}$ is passed into 500 g of liquid water at $20^\circ\text{C}$ inside a calorimeter of negligible heat capacity.Given $L_v = 540\text{ cal/g}$ and $c_w = 1\text{ cal/g}^\circ\text{C}$, what is the final mass of liquid water in the container at equilibrium?

Prevost's Theory of Heat Exchange:Statement I: All bodies above absolute zero emit thermal radiation continuously.Statement II: A body in thermal equilibrium with its surroundings ceases radiation exchange.Which statement correctly describes a body in thermal equilibrium with its surroundings?

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In a calorimetry experiment, 40 g of ice at $0^\circ\text{C}$ is mixed with 40 g of liquid water at $40^\circ\text{C}$ in an insulated vessel.
Given latent heat of fusion $L_f = 80\text{ cal/g}$ and specific heat of water $c = 1\text{ cal/g}^\circ\text{C}$, what is the final state of the mixture?

A composite slab consists of two layers of equal thickness $d$ placed end to end with thermal conductivities $K_1 = 100\text{ W/m}\cdot\text{K}$ and $K_2 = 300\text{ W/m}\cdot\text{K}$.
What is the effective thermal conductivity $K_{eq}$ of the composite slab for series heat flow?

A pendulum clock with a brass rod ($\alpha = 2 \times 10^{-5}\text{ K}^{-1}$) keeps accurate time at $20^\circ\text{C}$.
If the ambient temperature increases to $30^\circ\text{C}$, how much time does the clock lose or gain per day?

On a frozen lake surface, an ice sheet of thickness 2 cm forms in 10 minutes when atmospheric temperature is $-10^\circ\text{C}$.
How much additional time is required for the ice layer to grow from a thickness of 2 cm to 4 cm?

A copper calorimeter of mass 100 g ($c_{Cu} = 0.1\text{ cal/g}^\circ\text{C}$) contains 140 g of water at $15^\circ\text{C}$.
If 50 g of water at $55^\circ\text{C}$ is added to the calorimeter, what is the final thermal equilibrium temperature?

A conducting rod of length $L$ and cross-sectional area $A$ has position-dependent thermal conductivity $K(x) = K_0 (1 + x/L)$ along its length.
If the ends at $x=0$ and $x=L$ are maintained at steady temperatures $T_1$ and $T_2$ ($T_1 > T_2$), what is the steady-state rate of heat flow $H$?

Dry steam at $100^\circ\text{C}$ is passed into 500 g of liquid water at $20^\circ\text{C}$ inside a calorimeter of negligible heat capacity.
Given $L_v = 540\text{ cal/g}$ and $c_w = 1\text{ cal/g}^\circ\text{C}$, what is the final mass of liquid water in the container at equilibrium?

Prevost's Theory of Heat Exchange:
Statement I: All bodies above absolute zero emit thermal radiation continuously.
Statement II: A body in thermal equilibrium with its surroundings ceases radiation exchange.
Which statement correctly describes a body in thermal equilibrium with its surroundings?