Grade 11 : Physics - Thermal Properties (Set 4)

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Grade 11 : Physics - Thermal Properties (Set 4)— Questions & Detailed Solutions

Thermometer Scale Lower Fixed Point (Ice Point) Upper Fixed Point (Steam Point)
Celsius ($^\circ\text{C}$) $0^\circ\text{C}$ $100^\circ\text{C}$
Custom Scale ($^\circ\text{X}$) $20^\circ\text{X}$ $170^\circ\text{X}$
A custom thermometer is calibrated according to the table above. If this custom thermometer reads $80^\circ\text{X}$, what is the equivalent temperature on the Celsius scale?

Thermometer Scale	Lower Fixed Point (Ice Point)	Upper Fixed Point (Steam Point)
Celsius ($^\circ\text{C}$)	$0^\circ\text{C}$	$100^\circ\text{C}$
Custom Scale ($^\circ\text{X}$)	$20^\circ\text{X}$	$170^\circ\text{X}$

(A)

35 °C

(B)

40 °C

(C)

45 °C

(D)

50 °C

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Using linear interpolation between fixed points:
$$\frac{X - \text{LFP}_X}{\text{UFP}_X - \text{LFP}_X} = \frac{C - 0}{100 - 0}$$$$\frac{80 - 20}{170 - 20} = \frac{C}{100} \implies \frac{60}{150} = \frac{C}{100} \implies C = 0.4 \times 100 = 40^\circ\text{C}.$$

[Composite Rod Setup: A steel section ($L_1 = 50cm$, $\alpha_1 = 1.2 \times 10^{-5}\text{ K}^{-1}$) joined end-to-end with a brass section ($L_2 = 40cm$, $\alpha_2 = 2.0 \times 10^{-5}\text{ K}^{-1}$)]
What is the total increase in length of the composite rod when its temperature is increased by 50 K?

(A)

0.5 mm

(B)

0.7 mm

(C)

0.9 mm

(D)

1.2 mm

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: The total expansion is the sum of expansions of both rods:
$$\Delta L = \Delta L_1 + \Delta L_2 = L_1 \alpha_1 \Delta T + L_2 \alpha_2 \Delta T$$$$\Delta L = (50 \times 1.2 \times 10^{-5} \times 50) + (40 \times 2.0 \times 10^{-5} \times 50)$$$$\Delta L = 0.030\text{ cm} + 0.040\text{ cm} = 0.070\text{ cm} = 0.7\text{ mm}.$$

A solid metal cube has a density of $8.0\text{ g/cm}^3$ at $0^\circ\text{C}$. The coefficient of cubical expansion of the metal is $\gamma = 4.0 \times 10^{-5}\text{ K}^{-1}$.
What is the density of the metal cube when heated to $100^\circ\text{C}$?

(A)

7.97 g/cm³

(B)

8.03 g/cm³

(C)

7.68 g/cm³

(D)

7.85 g/cm³

View Correct Answer & Detailed Solution

✓ Correct Option: (A)

Explanation: Density varies with temperature according to:
$$\rho' = \frac{\rho_0}{1 + \gamma \Delta T}$$$$\rho' = \frac{8.0}{1 + (4.0 \times 10^{-5} \times 100)} = \frac{8.0}{1.004} \approx 7.968\text{ g/cm}^3 \approx 7.97\text{ g/cm}^3.$$

Property Value
Real expansion coefficient of liquid ($\gamma_r$) $6.5 \times 10^{-4}\text{ K}^{-1}$
Volume expansion coefficient of glass ($\gamma_g$) $1.5 \times 10^{-5}\text{ K}^{-1}$
A glass vessel is filled with liquid. Based on the expansion coefficients provided above, what is the coefficient of apparent expansion ($\gamma_a$) of the liquid?

Property	Value
Real expansion coefficient of liquid ($\gamma_r$)	$6.5 \times 10^{-4}\text{ K}^{-1}$
Volume expansion coefficient of glass ($\gamma_g$)	$1.5 \times 10^{-5}\text{ K}^{-1}$

(A)

$6.65 \times 10^{-4}\text{ K}^{-1}$

(B)

$6.35 \times 10^{-4}\text{ K}^{-1}$

(C)

$5.00 \times 10^{-4}\text{ K}^{-1}$

(D)

$8.00 \times 10^{-4}\text{ K}^{-1}$

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: The apparent coefficient of expansion is given by:
$$\gamma_a = \gamma_r - \gamma_g$$$$\gamma_a = (6.5 \times 10^{-4}) - (0.15 \times 10^{-4}) = 6.35 \times 10^{-4}\text{ K}^{-1}.$$

In a calorimetry experiment, 10 g of ice at $0^\circ\text{C}$ is mixed with 10 g of steam at $100^\circ\text{C}$ in an insulated vessel. Given: latent heat of fusion $L_f = 80\text{ cal/g}$, latent heat of vaporization $L_v = 540\text{ cal/g}$, specific heat of water $c = 1\text{ cal/g}\cdot^\circ\text{C}$.
What is the final equilibrium temperature of the mixture?

(A)

50 °C

(B)

80 °C

(C)

100 °C

(D)

0 °C

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: Heat required to melt ice and heat water to $100^\circ\text{C}$:
$$Q_{\text{req}} = (10 \times 80) + (10 \times 1 \times 100) = 800 + 1000 = 1800\text{ cal}.$$Heat released by complete condensation of steam:
$$Q_{\text{steam}} = 10 \times 540 = 5400\text{ cal}.$$Since $Q_{\text{steam}} > Q_{\text{req}}$, only a fraction of steam condenses, maintaining equilibrium at $100^\circ\text{C}$.

[Calorimeter diagram: Water equivalent $W = 20g$, containing $m_w = 180g$ of water at $T_i = 20^\circ\text{C}$. Metal sample $m_m = 100g$ dropped at $T_m = 100^\circ\text{C}$. Final equilibrium temperature $T_f = 25^\circ\text{C}$.]
What is the specific heat capacity of the metal sample?

(A)

0.100 cal/g°C

(B)

0.133 cal/g°C

(C)

0.250 cal/g°C

(D)

0.400 cal/g°C

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: By principle of calorimetry:
$$\text{Heat lost by metal} = \text{Heat gained by (water + calorimeter)}$$$$100 \times c_m \times (100 - 25) = (180 + 20) \times 1 \times (25 - 20)$$$$7500 c_m = 200 \times 5 = 1000 \implies c_m = \frac{1000}{7500} = \frac{2}{15} \approx 0.133\text{ cal/g}^\circ\text{C}.$$

[Composite Slab Diagram: Layer A ($K_A = 200\text{ W/m}\cdot\text{K}$, thickness $d$) joined to Layer B ($K_B = 100\text{ W/m}\cdot\text{K}$, thickness $d$). Left surface at $100^\circ\text{C}$, right surface at $0^\circ\text{C}$.]
Under steady-state heat conduction, what is the temperature $T_{\text{int}}$ at the interface between Layer A and Layer B?

(A)

50.0 °C

(B)

66.7 °C

(C)

33.3 °C

(D)

75.0 °C

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Equal heat current flows through both layers at steady state:
$$\frac{K_A A (100 - T_{\text{int}})}{d} = \frac{K_B A (T_{\text{int}} - 0)}{d}$$$$200 (100 - T_{\text{int}}) = 100 T_{\text{int}} \implies 20000 = 300 T_{\text{int}} \implies T_{\text{int}} = \frac{200}{3} \approx 66.7^\circ\text{C}.$$

[Parallel Rods Diagram: Rod X ($K_X = K$) and Rod Y ($K_Y = 3K$) connected in parallel between reservoirs at $100^\circ\text{C}$ and $20^\circ\text{C}$. Both rods have identical length and cross-sectional area.]
If the rate of heat conduction through rod X is 15 W, what is the total rate of heat flow through the parallel combination?

(A)

30 W

(B)

45 W

(C)

60 W

(D)

75 W

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: For rod X: $H_X = \frac{K A \Delta T}{L} = 15\text{ W}$.
For rod Y: $H_Y = \frac{(3K) A \Delta T}{L} = 3 H_X = 45\text{ W}$.
Total heat flow rate: $H_{\text{total}} = H_X + H_Y = 15 + 45 = 60\text{ W}$.

A copper rod has length $L = 0.5m$, cross-sectional area $A = 10^{-4}m^2$, and thermal conductivity $K = 400\text{ W/m}\cdot\text{K}$.
What is the thermal resistance of this copper rod?

(A)

6.25 K/W

(B)

12.5 K/W

(C)

25.0 K/W

(D)

50.0 K/W

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Thermal resistance is defined as:
$$R_{\text{th}} = \frac{L}{K A} = \frac{0.5}{400 \times 10^{-4}} = \frac{0.5}{0.04} = 12.5\text{ K/W}.$$

Q10

A body cools from $80^\circ\text{C}$ to $60^\circ\text{C}$ in 5 minutes in a room kept at a constant temperature of $20^\circ\text{C}$.
According to Newton's law of cooling, how long will it take for the body to cool from $60^\circ\text{C}$ to $40^\circ\text{C}$ in the same room?

(A)

5.00 minutes

(B)

6.67 minutes

(C)

8.33 minutes

(D)

10.00 minutes

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: Case 1: $\frac{80-60}{5} = k\left(\frac{80+60}{2} - 20\right) \implies 4 = k(50) \implies k = 0.08\text{ min}^{-1}$.
Case 2: $\frac{60-40}{t} = k\left(\frac{60+40}{2} - 20\right) \implies \frac{20}{t} = 0.08(30) = 2.4$.
$$t = \frac{20}{2.4} = \frac{25}{3} \approx 8.33\text{ minutes}.$$

Q11

Two spherical black bodies A and B have radii $R_A = 2cm$ and $R_B = 4cm$, and absolute surface temperatures $T_A = 600\text{ K}$ and $T_B = 300\text{ K}$.
What is the ratio of total thermal power radiated by body A to body B ($P_A / P_B$)?

(A)

(B)

(C)

(D)

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: By Stefan-Boltzmann Law, $P = \sigma A T^4 = \sigma (4\pi R^2) T^4$:
$$\frac{P_A}{P_B} = \left(\frac{R_A}{R_B}\right)^2 \left(\frac{T_A}{T_B}\right)^4 = \left(\frac{2}{4}\right)^2 \left(\frac{600}{300}\right)^4 = \left(\frac{1}{2}\right)^2 \times 2^4 = \frac{1}{4} \times 16 = 4.$$

Q12

Celestial Body Peak Wavelength ($\lambda_m$)
Star 1 400 nm
Star 2 600 nm
Using Wien's displacement law, determine the ratio of the absolute surface temperature of Star 1 to Star 2 ($T_1 / T_2$).

Celestial Body	Peak Wavelength ($\lambda_m$)
Star 1	400 nm
Star 2	600 nm

(A)

0.67

(B)

1.25

(C)

1.50

(D)

2.25

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: Wien's law states $\lambda_m T = b \implies T \propto \frac{1}{\lambda_m}$.
$$\frac{T_1}{T_2} = \frac{\lambda_{m2}}{\lambda_{m1}} = \frac{600\text{ nm}}{400\text{ nm}} = 1.50.$$

Q13

A glass window pane has an area of $1.5m^2$ and thickness of 6 mm. The indoor temperature is maintained at $22^\circ\text{C}$ while the outdoor temperature is $2^\circ\text{C}$. The thermal conductivity of glass is $0.8\text{ W/m}\cdot\text{K}$.
Calculate the rate of conductive heat loss through the glass window pane.

(A)

1000 W

(B)

2000 W

(C)

4000 W

(D)

6000 W

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: The rate of heat transfer is:
$$H = \frac{K A \Delta T}{d} = \frac{0.8 \times 1.5 \times (22 - 2)}{6 \times 10^{-3}} = \frac{1.2 \times 20}{0.006} = \frac{24}{0.006} = 4000\text{ W} = 4\text{ kW}.$$

Q14

A pendulum clock regulated by a brass rod (linear expansion coefficient $\alpha = 2.0 \times 10^{-5}\text{ K}^{-1}$) keeps correct time at $20^\circ\text{C}$.
If the ambient temperature rises to $30^\circ\text{C}$, how many seconds per day will the clock lose?

(A)

4.32 seconds

(B)

8.64 seconds

(C)

17.28 seconds

(D)

21.60 seconds

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Fractional change in time period is $\frac{\Delta T}{T} = \frac{1}{2} \alpha \Delta \theta$.
$$\frac{\Delta T}{T} = \frac{1}{2} \times (2.0 \times 10^{-5}) \times (30 - 20) = 10^{-4}.$$Time lost per day (86400 s):
$$\text{Loss} = 10^{-4} \times 86400 = 8.64\text{ seconds}.$$

Q15

A steel rod of cross-sectional area $2.0cm^2$ is rigidly clamped between two rigid supports at $30^\circ\text{C}$. The temperature drops to $10^\circ\text{C}$. Given: Young's modulus $Y = 2.0 \times 10^{11}\text{ N/m}^2$, $\alpha = 1.1 \times 10^{-5}\text{ K}^{-1}$.
What thermal force is exerted by the rod on the rigid clamps?

(A)

4400 N

(B)

8800 N

(C)

17600 N

(D)

22000 N

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Thermal stress $= Y \alpha \Delta T = (2.0 \times 10^{11}) \times (1.1 \times 10^{-5}) \times 20 = 4.4 \times 10^7\text{ N/m}^2$.
Thermal force $F = \text{Stress} \times A$:
$$F = (4.4 \times 10^7) \times (2.0 \times 10^{-4}\text{ m}^2) = 8800\text{ N}.$$

Q16

Parameter Value
Mass of Liquid 200 g
Initial Temperature $15^\circ\text{C}$
Heater Electrical Power 50 W
Heating Duration 4 minutes
Final Temperature $45^\circ\text{C}$
Neglecting heat losses to surroundings and container, what is the specific heat capacity of the liquid in $\text{J/(g}\cdot\text{K)}$?

Parameter	Value
Mass of Liquid	200 g
Initial Temperature	$15^\circ\text{C}$
Heater Electrical Power	50 W
Heating Duration	4 minutes
Final Temperature	$45^\circ\text{C}$

(A)

1.0 J/(g·K)

(B)

1.5 J/(g·K)

(C)

2.0 J/(g·K)

(D)

2.5 J/(g·K)

View Correct Answer & Detailed Solution

✓ Correct Option: (C)

Explanation: Electrical energy supplied:
$$Q = P \times t = 50 \times (4 \times 60) = 12000\text{ J}.$$By calorimetry, $Q = m c \Delta T$:
$$12000 = 200 \times c \times (45 - 15) \implies 12000 = 6000 c \implies c = 2.0\text{ J/(g}\cdot\text{K)}.$$

Q17

An electric kettle with power rating 1.0 kW contains 0.5 kg of water at $100^\circ\text{C}$. Latent heat of vaporization of water $L_v = 2.26 \times 10^6\text{ J/kg}$.
How long will it take to completely convert all the boiling water into steam?

(A)

565 s

(B)

1130 s

(C)

2260 s

(D)

3390 s

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Total heat required for vaporization:
$$Q = m L_v = 0.5 \times (2.26 \times 10^6) = 1.13 \times 10^6\text{ J}.$$Time required $t = \frac{Q}{P}$:
$$t = \frac{1.13 \times 10^6}{1000} = 1130\text{ seconds}.$$

Q18

A black body of emissivity $\epsilon = 1.0$ and surface area $A = 0.5m^2$ is at temperature 300 K in surroundings at absolute zero (0 K). Stefan-Boltzmann constant $\sigma = 5.67 \times 10^{-8}\text{ W/m}^2\cdot\text{K}^4$.
What is the net rate of radiative heat energy emitted by the surface?

(A)

114.8 W

(B)

229.6 W

(C)

459.3 W

(D)

918.5 W

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: By Stefan's law:
$$P = \sigma A T^4 = (5.67 \times 10^{-8}) \times 0.5 \times (300)^4$$$$P = 2.835 \times 10^{-8} \times (8.1 \times 10^9) = 2.835 \times 81 \approx 229.6\text{ W}.$$

Q19

[Bar Conduction Profile: A uniform metal rod has its left boundary fixed at $100^\circ\text{C}$ and right boundary fixed at $0^\circ\text{C}$. The steady-state temperature gradient along the rod is $-2.5^\circ\text{C/cm}$.]
What is the total length $L$ of the metal rod?

(A)

25 cm

(B)

40 cm

(C)

50 cm

(D)

80 cm

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Temperature gradient magnitude is given by:
$$\left|\frac{dT}{dx}\right| = \frac{\Delta T}{L} \implies 2.5^\circ\text{C/cm} = \frac{100 - 0}{L}$$$$L = \frac{100}{2.5} = 40\text{ cm}.$$

Q20

[Circular Copper Plate: Central circular hole of diameter $d = 4.0cm$ at $20^\circ\text{C}$. Linear thermal expansion coefficient $\alpha = 1.7 \times 10^{-5}\text{ K}^{-1}$. Heated to $120^\circ\text{C}$.]
What happens to the diameter of the central hole when the plate is heated to $120^\circ\text{C}$?

(A)

It decreases by 0.068 mm

(B)

It increases by 0.068 mm

(C)

It remains unchanged

(D)

It decreases by 0.136 mm

View Correct Answer & Detailed Solution

✓ Correct Option: (B)

Explanation: Internal voids expand thermal-wise identically as solid material:
$$\Delta d = d_0 \alpha \Delta T = (4.0\text{ cm}) \times (1.7 \times 10^{-5}) \times (100) = 6.8 \times 10^{-3}\text{ cm} = 0.068\text{ mm}.$$The hole diameter increases by 0.068 mm.

Grade 11 : Physics - Thermal Properties (Set 4)

Grade 11 : Physics - Thermal Properties (Set 4)— Questions & Detailed Solutions

A solid metal cube has a density of $8.0\text{ g/cm}^3$ at $0^\circ\text{C}$. The coefficient of cubical expansion of the metal is $\gamma = 4.0 \times 10^{-5}\text{ K}^{-1}$.
What is the density of the metal cube when heated to $100^\circ\text{C}$?

[Calorimeter diagram: Water equivalent $W = 20g$, containing $m_w = 180g$ of water at $T_i = 20^\circ\text{C}$. Metal sample $m_m = 100g$ dropped at $T_m = 100^\circ\text{C}$. Final equilibrium temperature $T_f = 25^\circ\text{C}$.]
What is the specific heat capacity of the metal sample?

A copper rod has length $L = 0.5m$, cross-sectional area $A = 10^{-4}m^2$, and thermal conductivity $K = 400\text{ W/m}\cdot\text{K}$.
What is the thermal resistance of this copper rod?

A body cools from $80^\circ\text{C}$ to $60^\circ\text{C}$ in 5 minutes in a room kept at a constant temperature of $20^\circ\text{C}$.
According to Newton's law of cooling, how long will it take for the body to cool from $60^\circ\text{C}$ to $40^\circ\text{C}$ in the same room?

Two spherical black bodies A and B have radii $R_A = 2cm$ and $R_B = 4cm$, and absolute surface temperatures $T_A = 600\text{ K}$ and $T_B = 300\text{ K}$.
What is the ratio of total thermal power radiated by body A to body B ($P_A / P_B$)?

Celestial Body Peak Wavelength ($\lambda_m$)
Star 1 400 nm
Star 2 600 nm
Using Wien's displacement law, determine the ratio of the absolute surface temperature of Star 1 to Star 2 ($T_1 / T_2$).

A pendulum clock regulated by a brass rod (linear expansion coefficient $\alpha = 2.0 \times 10^{-5}\text{ K}^{-1}$) keeps correct time at $20^\circ\text{C}$.
If the ambient temperature rises to $30^\circ\text{C}$, how many seconds per day will the clock lose?

An electric kettle with power rating 1.0 kW contains 0.5 kg of water at $100^\circ\text{C}$. Latent heat of vaporization of water $L_v = 2.26 \times 10^6\text{ J/kg}$.
How long will it take to completely convert all the boiling water into steam?

A black body of emissivity $\epsilon = 1.0$ and surface area $A = 0.5m^2$ is at temperature 300 K in surroundings at absolute zero (0 K). Stefan-Boltzmann constant $\sigma = 5.67 \times 10^{-8}\text{ W/m}^2\cdot\text{K}^4$.
What is the net rate of radiative heat energy emitted by the surface?

[Bar Conduction Profile: A uniform metal rod has its left boundary fixed at $100^\circ\text{C}$ and right boundary fixed at $0^\circ\text{C}$. The steady-state temperature gradient along the rod is $-2.5^\circ\text{C/cm}$.]
What is the total length $L$ of the metal rod?

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Grade 11 : Physics - Thermal Properties (Set 4)

Grade 11 : Physics - Thermal Properties (Set 4)— Questions & Detailed Solutions

A solid metal cube has a density of $8.0\text{ g/cm}^3$ at $0^\circ\text{C}$. The coefficient of cubical expansion of the metal is $\gamma = 4.0 \times 10^{-5}\text{ K}^{-1}$.What is the density of the metal cube when heated to $100^\circ\text{C}$?

[Calorimeter diagram: Water equivalent $W = 20g$, containing $m_w = 180g$ of water at $T_i = 20^\circ\text{C}$. Metal sample $m_m = 100g$ dropped at $T_m = 100^\circ\text{C}$. Final equilibrium temperature $T_f = 25^\circ\text{C}$.]What is the specific heat capacity of the metal sample?

A copper rod has length $L = 0.5m$, cross-sectional area $A = 10^{-4}m^2$, and thermal conductivity $K = 400\text{ W/m}\cdot\text{K}$.What is the thermal resistance of this copper rod?

A body cools from $80^\circ\text{C}$ to $60^\circ\text{C}$ in 5 minutes in a room kept at a constant temperature of $20^\circ\text{C}$.According to Newton's law of cooling, how long will it take for the body to cool from $60^\circ\text{C}$ to $40^\circ\text{C}$ in the same room?

Two spherical black bodies A and B have radii $R_A = 2cm$ and $R_B = 4cm$, and absolute surface temperatures $T_A = 600\text{ K}$ and $T_B = 300\text{ K}$.What is the ratio of total thermal power radiated by body A to body B ($P_A / P_B$)?

Celestial BodyPeak Wavelength ($\lambda_m$)Star 1400 nmStar 2600 nmUsing Wien's displacement law, determine the ratio of the absolute surface temperature of Star 1 to Star 2 ($T_1 / T_2$).

A pendulum clock regulated by a brass rod (linear expansion coefficient $\alpha = 2.0 \times 10^{-5}\text{ K}^{-1}$) keeps correct time at $20^\circ\text{C}$.If the ambient temperature rises to $30^\circ\text{C}$, how many seconds per day will the clock lose?

ParameterValueMass of Liquid200 gInitial Temperature$15^\circ\text{C}$Heater Electrical Power50 WHeating Duration4 minutesFinal Temperature$45^\circ\text{C}$Neglecting heat losses to surroundings and container, what is the specific heat capacity of the liquid in $\text{J/(g}\cdot\text{K)}$?

An electric kettle with power rating 1.0 kW contains 0.5 kg of water at $100^\circ\text{C}$. Latent heat of vaporization of water $L_v = 2.26 \times 10^6\text{ J/kg}$.How long will it take to completely convert all the boiling water into steam?

A black body of emissivity $\epsilon = 1.0$ and surface area $A = 0.5m^2$ is at temperature 300 K in surroundings at absolute zero (0 K). Stefan-Boltzmann constant $\sigma = 5.67 \times 10^{-8}\text{ W/m}^2\cdot\text{K}^4$.What is the net rate of radiative heat energy emitted by the surface?

[Bar Conduction Profile: A uniform metal rod has its left boundary fixed at $100^\circ\text{C}$ and right boundary fixed at $0^\circ\text{C}$. The steady-state temperature gradient along the rod is $-2.5^\circ\text{C/cm}$.]What is the total length $L$ of the metal rod?

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A solid metal cube has a density of $8.0\text{ g/cm}^3$ at $0^\circ\text{C}$. The coefficient of cubical expansion of the metal is $\gamma = 4.0 \times 10^{-5}\text{ K}^{-1}$.
What is the density of the metal cube when heated to $100^\circ\text{C}$?

[Calorimeter diagram: Water equivalent $W = 20g$, containing $m_w = 180g$ of water at $T_i = 20^\circ\text{C}$. Metal sample $m_m = 100g$ dropped at $T_m = 100^\circ\text{C}$. Final equilibrium temperature $T_f = 25^\circ\text{C}$.]
What is the specific heat capacity of the metal sample?

A copper rod has length $L = 0.5m$, cross-sectional area $A = 10^{-4}m^2$, and thermal conductivity $K = 400\text{ W/m}\cdot\text{K}$.
What is the thermal resistance of this copper rod?

A body cools from $80^\circ\text{C}$ to $60^\circ\text{C}$ in 5 minutes in a room kept at a constant temperature of $20^\circ\text{C}$.
According to Newton's law of cooling, how long will it take for the body to cool from $60^\circ\text{C}$ to $40^\circ\text{C}$ in the same room?

Two spherical black bodies A and B have radii $R_A = 2cm$ and $R_B = 4cm$, and absolute surface temperatures $T_A = 600\text{ K}$ and $T_B = 300\text{ K}$.
What is the ratio of total thermal power radiated by body A to body B ($P_A / P_B$)?

Celestial Body Peak Wavelength ($\lambda_m$)
Star 1 400 nm
Star 2 600 nm
Using Wien's displacement law, determine the ratio of the absolute surface temperature of Star 1 to Star 2 ($T_1 / T_2$).

A pendulum clock regulated by a brass rod (linear expansion coefficient $\alpha = 2.0 \times 10^{-5}\text{ K}^{-1}$) keeps correct time at $20^\circ\text{C}$.
If the ambient temperature rises to $30^\circ\text{C}$, how many seconds per day will the clock lose?

An electric kettle with power rating 1.0 kW contains 0.5 kg of water at $100^\circ\text{C}$. Latent heat of vaporization of water $L_v = 2.26 \times 10^6\text{ J/kg}$.
How long will it take to completely convert all the boiling water into steam?

A black body of emissivity $\epsilon = 1.0$ and surface area $A = 0.5m^2$ is at temperature 300 K in surroundings at absolute zero (0 K). Stefan-Boltzmann constant $\sigma = 5.67 \times 10^{-8}\text{ W/m}^2\cdot\text{K}^4$.
What is the net rate of radiative heat energy emitted by the surface?

[Bar Conduction Profile: A uniform metal rod has its left boundary fixed at $100^\circ\text{C}$ and right boundary fixed at $0^\circ\text{C}$. The steady-state temperature gradient along the rod is $-2.5^\circ\text{C/cm}$.]
What is the total length $L$ of the metal rod?