Temperature, Heat and Internal Energy: Practice Questions

An insulated calorimeter of heat capacity \(120\text{ J }^\circ\text{C}^{-1}\) contains \(250\text{ g}\) of water at \(30^\circ\text{C}\). A block of ice of mass \(150\text{ g}\) at \(-20^\circ\text{C}\) is placed into the calorimeter. Which of the following best describes the final state of the mixture when thermal equilibrium is reached?

An electric heater of power \( 50 \text{ W} \) is used to heat \( 0.4 \text{ kg} \) of a certain liquid in a container. The temperature of the liquid increases from \( 20^{\circ}\text{C} \) to \( 40^{\circ}\text{C} \) in \( 10 \text{ minutes} \). The room temperature is \( 20^{\circ}\text{C} \). When the heater is switched off at \( 40^{\circ}\text{C} \), the liquid is found to cool at an initial rate of \( 0.8^{\circ}\text{C min}^{-1} \). Assuming the rate of heat loss to the surroundings is proportional to the temperature difference between the liquid and the room and the heat capacity of the container is negligible, what is the specific heat capacity of the liquid?

An experiment is carried out in a laboratory at a constant ambient temperature of \(20^\text{o} \text{C}\) to determine the constant power \(P\) of an electric heater and the heat loss coefficient \(k\) of the container. The heater is fully immersed in \(0.40 \text{ kg}\) of ice, initially at \(0^\text{o} \text{C}\).

It is observed that the ice takes \(526 \text{ s}\) to melt completely (Stage 1). The resulting water then takes an additional \(30.7 \text{ s}\) to warm up from \(0^\text{o} \text{C}\) to \(5.0^\text{o} \text{C}\) (Stage 2).

Assume the rate of heat loss \(H_L\) to the surroundings is proportional to the temperature difference \(\Delta T\) between the substance and the surroundings, such that \(H_L = k \Delta T\). For calculating the average heat loss in Stage 2, the average temperature of the water can be taken as \(2.5^\text{o} \text{C}\).

Given: Specific latent heat of fusion of ice \(l_f = 3.34 \times 10^5 \text{ J kg}^{-1}\), Specific heat capacity of water \(c_w = 4200 \text{ J kg}^{-1} \text{ K}^{-1}\).

Determine the constant power \(P\) of the heater and the proportionality constant \(k\) (in \(\text{W K}^{-1}\)), rounded to three significant figures.

A student uses an electric heater of constant power to heat a certain volume of water in a well-insulated calorimeter. The temperature of the water and the calorimeter increases by \(10^\circ\text{C}\) in \(200\text{ s}\). When the experiment is repeated under the same conditions but with the volume of water doubled, the same temperature increase of \(10^\circ\text{C}\) takes \(350\text{ s}\). Find the ratio of the heat capacity of the calorimeter to the heat capacity of the original volume of water.

An insulated container of unknown heat capacity \( C \) is used to heat a liquid with specific heat capacity \( c \). In the first experiment, \( 0.5 \text{ kg} \) of the liquid is heated from \( 20^{\circ}\text{C} \) to \( 50^{\circ}\text{C} \) in \( 330 \text{ s} \) using a \( 100 \text{ W} \) immersion heater. In the second experiment, \( 1.0 \text{ kg} \) of the same liquid is heated from \( 20^{\circ}\text{C} \) to \( 40^{\circ}\text{C} \) in \( 420 \text{ s} \) using the same heater. Assuming that there is no heat loss to the surroundings, find the heat capacity \( C \) of the container.

Water is commonly used as a coolant in the cooling systems of car engines. Identify the specific thermal property of water that makes it suitable for this role and explain its advantage.

One kilogram of saturated liquid ethanol is entirely converted to vapor at its boiling point under constant atmospheric pressure ( \(1.01 \times 10^5\text{ Pa}\)). If the specific latent heat of vaporization is \(841\text{ kJ kg}^{-1}\) and the volume expands by \(0.45\text{ m}^3\), calculate the increase in the internal energy of the ethanol during this process and state the primary reason why this increase is less than the heat supplied.

A fixed mass of liquid water is vaporized into steam at a constant temperature of \(100^\circ\text{C}\) under standard atmospheric pressure. Explain why the latent heat of vaporization \((L_v)\) is significantly greater than the increase in the internal energy (\(\Delta U\)) of the substance, making specific reference to the microscopic interpretation of energy transfer during this process.

A student uses an electric heater to warm up a \(0.60\text{ kg}\) sample of water from an initial temperature of \(25^\circ\text{C}\) to a final temperature of \(75^\circ\text{C}\).

(Given: Specific heat capacity of water \(c_{\text{water}} = 4200\text{ J kg}^{-1}\text{ K}^{-1}\))

(a) State the definition of specific heat capacity.

(b) Calculate the heat energy absorbed by the water.

(c) Explain how the internal energy of the water changes during this heating process, in terms of the kinetic and potential energies of its molecules.

A student conducts an experiment to investigate the thermal properties of substances. She mixes \(0.5\text{ kg}\) of water at \(80^\circ\text{C}\) with \(1.2\text{ kg}\) of a liquid Y at \(20^\circ\text{C}\) in a well-insulated container. Assume no heat is lost to the surroundings or the container.

(Given: Specific heat capacity of water \(c_w = 4200\text{ J kg}^{-1}\text{ K}^{-1}\); Specific heat capacity of liquid Y \(c_y = 2000\text{ J kg}^{-1}\text{ K}^{-1}\))

(a) Define the internal energy of the water in terms of the microscopic motion and arrangement of its molecules.

(b) Calculate the final temperature of the mixture when thermal equilibrium is reached.

(c) Explain why the high specific heat capacity of water makes it suitable for use in the cooling systems of car engines.