Practice Questions

Justify why water is an excellent coolant for automobile radiators compared to an oil with a specific heat capacity of $1965 \text{ J kg}^{-1} \text{ K}^{-1}$.

Calculate the amount of heat energy required to raise the temperature of $500 \text{ g}$ of copper from $25^{\circ}\text{C}$ to $125^{\circ}\text{C}$. The specific heat capacity of copper is $s = 386.4 \text{ J kg}^{-1}\text{K}^{-1}$.

List the three distinct modes of heat transfer.

A cylinder contains $2$ moles of an ideal gas at a temperature of $27^\circ\text{C}$ and a pressure of $1.5 \times 10^5$ Pa. Calculate the volume of the gas. (Universal gas constant $R = 8.31 \text{ J mol}^{-1} \text{K}^{-1}$).

Contrast the mechanisms of heat transfer by conduction and convection, highlighting the key difference in how energy is transported in each process.

Define heat.

Define heat and temperature, and state the SI unit for each.

Justify why burns from steam at $100^{\circ} \text{C}$ are more severe than burns from boiling water at the same temperature.

Calculate the total heat required to completely melt $50 \text{ g}$ of ice initially at $0^{\circ}\text{C}$. The latent heat of fusion of ice is $L_f = 3.33 \times 10^5 \text{ J kg}^{-1}$.

Recall the formula that relates the Celsius temperature scale ($t_C$) and the Fahrenheit temperature scale ($t_F$).

Justify why burns from steam at $100^{\circ}\text{C}$ are generally more severe than burns from boiling water at the same temperature.

Recall the ideal gas equation and name each variable and the constant involved.

Critique the use of a standard mercury-in-glass thermometer for accurately measuring temperatures approaching absolute zero. Justify your reasoning based on the thermal properties of mercury.

Evaluate the statement: 'A body with a high thermal conductivity is always a poor thermal insulator.' Justify your evaluation with reference to the definition of thermal conductivity.

A $500$ g block of an unknown metal absorbs $1.95 \times 10^4$ J of heat, causing its temperature to rise from $25^\circ\text{C}$ to $125^\circ\text{C}$. Solve for the specific heat capacity of the metal.

Name the SI unit of temperature and define absolute zero.

Justify the anomalous expansion of water and explain its environmental significance for aquatic life.

Recall the ideal-gas equation and identify each term in the equation.

Calculate the temperature on the Fahrenheit scale corresponding to $25^\circ\text{C}$.

Define latent heat of fusion ($L_f$).

Examine why a person wearing dark-colored clothes feels warmer in the sun compared to a person wearing light-colored clothes.

Propose a method to reduce the thermal stress in long railway tracks during extreme summer heat, explaining the physics principle behind your proposal.

Recall the mathematical relationship used to convert a temperature from the Celsius scale ($t_C$) to the Fahrenheit scale ($t_F$).

Define specific heat capacity and state its SI unit.

A chef claims that food cooks faster in a pressure cooker because the increased pressure itself cooks the food. Critique this claim.

Recall the formula for the amount of heat ($Q$) required for a mass ($m$) of a substance to undergo a change of state.

An aluminum rod has a length of $2.0 \text{ m}$ at an initial temperature of $20^{\circ}\text{C}$. Calculate its new length if it is heated to $100^{\circ}\text{C}$. The coefficient of linear expansion for aluminum is $\alpha_l = 2.5 \times 10^{-5} \text{ K}^{-1}$.

Define thermal conductivity and state its SI unit.

Explain the fundamental principle of calorimetry.

Summarize Newton's law of cooling and provide its mathematical expression.

Explain why a blacksmith heats an iron ring before fitting it onto a wooden wheel.

Analyze why large bodies of water, like oceans, have a moderating effect on the climate of nearby land areas, based on the concept of specific heat capacity.

Describe the key differences between the heat transfer mechanisms of conduction and convection.

Explain what is meant by the latent heat of fusion.

Recall Newton's law of cooling and explain the relationship it describes.

Compare the severity of a burn caused by $1 \text{ g}$ of steam at $100^{\circ}\text{C}$ with a burn caused by $1 \text{ g}$ of boiling water at $100^{\circ}\text{C}$.

Formulate a hypothesis explaining why cooking is faster in a pressure cooker, especially at high altitudes. Your explanation must connect boiling point, pressure, and heat transfer.

Two rods, one of copper and one of steel, of the same length and cross-section, are joined end-to-end. The free end of the copper is at $100^{\circ} \text{C}$ and the free end of the steel is at $0^{\circ} \text{C}$. Critique the assumption that the temperature gradient (change in temperature per unit length) will be the same in both rods.

A hollow metal sphere is heated uniformly. Evaluate how the volume of the empty cavity inside the sphere changes. Justify your conclusion using the principles of thermal expansion.

Summarize the three modes of heat transfer: conduction, convection, and radiation. Describe the primary mechanism for each.

Explain why land breezes and sea breezes occur in coastal areas.

Explain the principle of calorimetry.

Define the coefficient of linear expansion ($\alpha_l$) and state its SI unit.

Explain why a blacksmith heats an iron ring before fitting it onto the rim of a wooden wheel.

Describe the concepts of melting point and boiling point. Explain why the temperature of a substance remains constant during a change of state.

Calculate the temperature at which the reading on the Fahrenheit scale is exactly double the reading on the Celsius scale.

Analyze why land heats up faster than the sea during the daytime, leading to the formation of a sea breeze.

A sample of gas has a volume of $2.0 \text{ L}$ at a pressure of $1.0 \times 10^5 \text{ Pa}$ and a temperature of $27^{\circ}\text{C}$. Apply the combined gas law to find its volume if the pressure is increased to $2.0 \times 10^5 \text{ Pa}$ and the temperature is increased to $127^{\circ}\text{C}$.

The radiation emitted from a distant star has a peak intensity at a wavelength of $500 \text{ nm}$. Apply Wien's displacement law to calculate the surface temperature of the star. (Wien's constant $b = 2.9 \times 10^{-3} \text{ m K}$).

A body cools from $80^{\circ}\text{C}$ to $70^{\circ}\text{C}$ in 5 minutes. The temperature of the surroundings is $30^{\circ}\text{C}$. Solve for the time it will take to cool from $60^{\circ}\text{C}$ to $50^{\circ}\text{C}$, assuming Newton's law of cooling is applicable.

Analyze how the anomalous expansion of water, specifically its maximum density at $4^{\circ}\text{C}$, is crucial for the survival of aquatic life in lakes and ponds in cold climates.

Two spheres made of the same material have radii in the ratio $1:2$. If they are maintained at the same absolute temperature, compare the rates at which they radiate energy.

Design an experiment to determine the coefficient of linear expansion, $\alpha_l$, for an unknown metal rod. Justify your choice of apparatus and the procedure to ensure accuracy.

Propose a design modification for a standard calorimeter to further minimize heat loss by radiation, beyond just having polished surfaces. Justify your proposal.

Design a simple, cost-effective solar water heater. Create a basic diagram and justify the choice of materials for the main components based on the principles of heat transfer.

A student finds that the cooling curve for a body initially at $150^{\circ} \text{C}$ in a room at $25^{\circ} \text{C}$ is not a perfect exponential decay. Critique the student's assumption that Newton's law of cooling should be perfectly accurate in this scenario.

Design an investigation to compare the emissivities of a polished silver surface, a matte black surface, and a white painted surface. Explain how you would evaluate the results.

Explain the concept of thermal expansion in solids, mentioning the three types.

Define specific heat capacity and state its SI unit.

A new temperature scale, the 'Z-scale' (Z), is proposed. On this scale, the freezing point of water is $50$ Z and the boiling point is $250$ Z. Formulate the conversion equation between the Z-scale temperature ($T_Z$) and the Celsius scale temperature ($t_C$).

Design a setup to demonstrate the phenomenon of regelation. Propose an explanation for why the wire passes through the ice without cutting it in half.

A custom temperature scale, the X scale, is defined such that the freezing point of water is $0^\circ \text{X}$ and the boiling point is $150^\circ \text{X}$. Calculate the temperature in degrees Celsius that corresponds to $60^\circ \text{X}$.

Analyze why a bimetallic strip made of steel and brass bends when heated, with the brass on the outer side of the curve. Use the coefficients of linear expansion to support your answer ($\alpha_{\text{steel}} = 1.2 \times 10^{-5} \text{ K}^{-1}$, $\alpha_{\text{brass}} = 1.8 \times 10^{-5} \text{ K}^{-1}$).

Analyze the consequence of water's anomalous expansion on aquatic life in cold climates. Explain what would happen if water did not exhibit this property.

A body cools from $80^\circ\text{C}$ to $70^\circ\text{C}$ in 5 minutes. If the temperature of the surroundings is $20^\circ\text{C}$, apply Newton's law of cooling to calculate the time it will take to cool from $60^\circ\text{C}$ to $50^\circ\text{C}$.

A spherical blackbody with a radius of $5$ cm is maintained at a temperature of $500$ K. Calculate the total power radiated by the sphere. (Stefan-Boltzmann constant $\sigma = 5.67 \times 10^{-8} \text{ W m}^{-2} \text{K}^{-4}$).

Compare the amount of energy required to melt $1$ kg of ice at $0^\circ\text{C}$ with the energy required to vaporize $1$ kg of water at $100^\circ\text{C}$. Analyze why burns from steam are generally more severe than burns from boiling water. (Use $L_f = 3.33 \times 10^5 \text{ J kg}^{-1}$ and $L_v = 22.6 \times 10^5 \text{ J kg}^{-1}$).

Justify the statement: 'The anomalous expansion of water is crucial for the survival of aquatic life in cold climates.' Formulate an argument explaining the physical processes involved.

A composite rod is made by joining an aluminum rod of length $20$ cm and a copper rod of length $20$ cm. Both rods have the same cross-sectional area. The free end of the aluminum rod is maintained at $100^\circ\text{C}$ and the free end of the copper rod is at $0^\circ\text{C}$. Solve for the temperature at the junction of the two rods in the steady state. (Thermal conductivity of Al, $K_{\text{Al}} = 205 \text{ W m}^{-1} \text{K}^{-1}$; Thermal conductivity of Cu, $K_{\text{Cu}} = 385 \text{ W m}^{-1} \text{K}^{-1}$).

A student proposes using alcohol instead of mercury in a thermometer designed for high-temperature measurements in a laboratory furnace, which can reach up to $500^{\circ}\text{C}$. Critique this proposal, evaluating the suitability of alcohol for this purpose.

Two rods, one of copper and one of steel, have the same length and cross-sectional area. They are joined end-to-end. The free end of the copper rod is at $100^{\circ}\text{C}$ and the free end of the steel rod is at $0^{\circ}\text{C}$. Evaluate which rod will have a steeper temperature gradient. Justify your answer.

Formulate a complete heat budget calculation to determine the total heat energy ($Q_{total}$) required to convert $m$ kg of ice initially at $-T_1^{\circ}\text{C}$ to steam at $T_2^{\circ}\text{C}$ (where $T_2 > 100$). Define all variables and create a step-by-step expression for the total heat.

Design a simple, low-cost solar water heater for domestic use. Propose materials for the key components and justify your choices based on the principles of heat transfer.

An engineer proposes building a bridge with single $20 \text{ m}$ steel beams without any expansion joints. Evaluate this proposal for a region where temperature varies from $-10^{\circ} \text{C}$ to $40^{\circ} \text{C}$. Calculate the thermal stress that would develop if the beam were rigidly fixed. Given: Young's modulus for steel $Y_{\text{steel}} = 2 \times 10^{11} \text{ N/m}^2$, and coefficient of linear expansion $\alpha_{\text{steel}} = 1.2 \times 10^{-5} \text{ K}^{-1}$.

Describe the anomalous expansion of water and explain its importance for aquatic life in cold climates.

Analyze how a bimetallic strip, made of steel and brass bonded together, functions as a thermal switch in a thermostat. Contrast its behavior when heated versus when cooled, given that the coefficient of linear expansion of brass ($\alpha_{brass} = 1.8 \times 10^{-5} \text{ K}^{-1}$) is greater than that of steel ($\alpha_{steel} = 1.2 \times 10^{-5} \text{ K}^{-1}$).

Calculate the total amount of heat energy required to convert $50$ g of ice at $-10^\circ\text{C}$ to steam at $100^\circ\text{C}$. (Given: $s_{\text{ice}} = 2100 \text{ J kg}^{-1} \text{K}^{-1}$, $s_{\text{water}} = 4186 \text{ J kg}^{-1} \text{K}^{-1}$, $L_f = 3.35 \times 10^5 \text{ J kg}^{-1}$, $L_v = 2.256 \times 10^6 \text{ J kg}^{-1}$).

Describe the anomalous behavior of water and explain its environmental significance.

A $200$ g copper block at $90^\circ\text{C}$ is placed in a $100$ g copper calorimeter containing $250$ g of water at $10^\circ\text{C}$. Assuming no heat is lost to the surroundings, calculate the final equilibrium temperature of the mixture. (Specific heat of copper $s_{\text{cu}} = 386 \text{ J kg}^{-1} \text{K}^{-1}$, specific heat of water $s_{\text{w}} = 4186 \text{ J kg}^{-1} \text{K}^{-1}$).

Formulate a mathematical model to calculate the final equilibrium temperature when a hot metal block of mass $m_1$, specific heat capacity $s_1$, and initial temperature $T_1$ is dropped into a calorimeter of mass $m_c$, specific heat capacity $s_c$, containing a liquid of mass $m_2$, specific heat capacity $s_2$, at an initial temperature $T_2$ (where $T_1 > T_2$). Propose the necessary assumptions for your model.

A manufacturer claims their new insulating material, 'ThermaBlock,' has a thermal conductivity of $0.001 \text{ J s}^{-1} \text{m}^{-1} \text{K}^{-1}$. Evaluate the feasibility of this claim by comparing it to the thermal conductivity of air.

A steel rod of length $1.5 \text{ m}$ and cross-sectional area $2.0 \times 10^{-4} \text{ m}^2$ is rigidly fixed between two supports. If the temperature is raised by $50^{\circ}\text{C}$, calculate the compressive stress developed in the rod. (Coefficient of linear expansion of steel $\alpha_{steel} = 1.2 \times 10^{-5} \text{ K}^{-1}$, Young's modulus of steel $Y_{steel} = 2.0 \times 10^{11} \text{ N m}^{-2}$)

A student performs an experiment to verify Newton's law of cooling. They plot a graph of temperature ($T$) versus time ($t$) and find it is an exponential decay curve, not a straight line. They conclude that Newton's law is incorrect. Critique the student's conclusion and propose the correct graphical analysis.

What is a blackbody? Summarize Wien's Displacement Law for blackbody radiation.

Two rods, one of copper and one of steel, have the same length $L$ and the same cross-sectional area $A$. They are joined end-to-end. The free end of the copper rod is maintained at $100^{\circ}\text{C}$ and the free end of the steel rod is at $0^{\circ}\text{C}$. Calculate the temperature at the junction of the two rods. (Thermal conductivity of copper $K_{cu} = 385 \text{ W m}^{-1}\text{K}^{-1}$, and steel $K_{steel} = 50.2 \text{ W m}^{-1}\text{K}^{-1}$)

An engineer needs to create a composite bar with a specific equivalent thermal conductivity. The bar is made by soldering two rods of different materials (Material A and Material B) end-to-end (in series). Both rods have the same length $L$ and cross-sectional area $A$. Formulate a general expression for the equivalent thermal conductivity $K_{eq}$ of the composite bar in terms of the thermal conductivities $K_A$ and $K_B$.

A $200 \text{ g}$ piece of iron at $90^{\circ}\text{C}$ is dropped into a $100 \text{ g}$ copper calorimeter containing $250 \text{ g}$ of water at $10^{\circ}\text{C}$. Solve for the final equilibrium temperature of the mixture, assuming no heat is lost to the surroundings. (Specific heat of iron $s_{iron} = 450 \text{ J kg}^{-1}\text{K}^{-1}$, copper $s_{cu} = 386 \text{ J kg}^{-1}\text{K}^{-1}$, and water $s_{water} = 4186 \text{ J kg}^{-1}\text{K}^{-1}$)

A steel rail of length $10$ m is laid on a railway track at a temperature of $20^\circ\text{C}$. Calculate the expansion gap that must be left between two rails to prevent buckling when the temperature rises to $50^\circ\text{C}$. If no gap is left, calculate the thermal stress developed. (Given $\alpha_{\text{steel}} = 1.2 \times 10^{-5} \text{ K}^{-1}$ and Young's modulus $Y_{\text{steel}} = 2 \times 10^{11} \text{ N m}^{-2}$).

Propose a method to determine the latent heat of vaporization ($L_v$) of an unknown liquid whose boiling point is approximately $80^{\circ} \text{C}$. Formulate the final equation for the calculation.

Design an experiment to determine the coefficient of linear expansion ($\alpha_l$) of an unknown metal rod. Justify the choice of apparatus and the procedure you would follow to ensure accuracy.