Heat and Thermodynamics

Which one of the following statements best defines the concept of heat ?

[amp_mcq option1=”The transformation of energy from one form to another” option2=”The conversion of energy into mass and vice-versa due to temperature difference” option3=”The transfer of energy due to temperature difference” option4=”The change in volume of a substance with temperature” correct=”option3″]

Heat is defined as the transfer of thermal energy between systems or objects of different temperatures. Energy naturally flows from a region of higher temperature to a region of lower temperature.

Heat is energy in transit, whereas temperature is a measure of the average kinetic energy of the particles within a substance. When there is a temperature difference between two objects or systems in thermal contact, energy is transferred between them, and this transferred energy is called heat.

The other options describe related concepts but not the definition of heat itself. Option A describes energy transformation (e.g., chemical to thermal). Option B relates to mass-energy equivalence and is not the definition of heat. Option D describes thermal expansion, which is a consequence of temperature change, not the definition of heat transfer.

A liquid is heated up to a certain temperature. Which one of the following situation would correspond to the boiling of the liquid?

[amp_mcq option1=”When atmospheric pressure becomes equal to the vapour pressure” option2=”When atmospheric pressure becomes less than vapour pressure” option3=”When atmospheric pressure becomes higher than the vapour pressure” option4=”When vapour pressure becomes equal to the air pressure” correct=”option1″]

A) When atmospheric pressure becomes equal to the vapour pressure corresponds to the boiling of the liquid.

– Boiling is the phase transition where a liquid turns into a gas when heated to its boiling point.
– The boiling point of a liquid is defined as the temperature at which its vapor pressure equals the surrounding environmental pressure (usually atmospheric pressure).
– At this point, the vapor pressure is sufficient to overcome the external pressure, allowing bubbles of vapor to form within the bulk of the liquid and rise to the surface.

– If atmospheric pressure is less than the vapor pressure at a given temperature, boiling occurs below the standard boiling point (e.g., at high altitudes).
– If atmospheric pressure is higher than the vapor pressure, boiling will not occur at that temperature; the liquid must be heated further to increase its vapor pressure to match the higher external pressure.
– Option D essentially states the same condition as option A, assuming “air pressure” refers to the external pressure, which is typically atmospheric pressure in an open system. Option A uses the more standard terminology.

Dry ice is used on a performing stage to produce mist in air. The process involved is an example of

[amp_mcq option1=”sublimation” option2=”evaporation” option3=”condensation” option4=”precipitation” correct=”option1″]

The correct answer is sublimation.

Dry ice is solid carbon dioxide. At atmospheric pressure, solid carbon dioxide changes directly into gaseous carbon dioxide without melting into a liquid. This process is called sublimation. The visible ‘mist’ produced when dry ice is used is actually water vapour in the surrounding air condensing or freezing due to the extremely cold carbon dioxide gas. However, the primary phase transition of the dry ice itself is sublimation, which drives the cooling effect leading to the mist formation.

Sublimation is an endothermic process, meaning it absorbs heat from the surroundings, which is why dry ice is so effective as a coolant and for creating effects like mist by cooling ambient water vapour.

A pressure cooker cooks food faster by

[amp_mcq option1=”increasing the boiling point of water” option2=”decreasing the boiling point of water” option3=”increasing the melting point of water” option4=”decreasing the melting point of water” correct=”option1″]

A pressure cooker works by sealing the cooking pot tightly, which prevents steam from escaping. As water heats up, it turns into steam, increasing the pressure inside the cooker. According to the relationship between pressure and boiling point, increasing the pressure on a liquid increases its boiling point.

By increasing the pressure inside, the boiling point of water is raised from 100°C (at standard atmospheric pressure) to a higher temperature, typically around 120-125°C. Food cooks faster at these higher temperatures.

Conversely, at high altitudes where atmospheric pressure is lower, water boils at temperatures below 100°C, which means food takes longer to cook compared to cooking at sea level. Pressure cookers counteract this effect or speed up cooking at any altitude by artificially increasing the pressure and thus the boiling point.

The temperature of a place on one sunny day is 113 in Fahrenheit scale. The Kelvin scale reading of this temperature will be

[amp_mcq option1=”318 K” option2=”45 K” option3=”62.8 K” option4=”335.8 K” correct=”option1″]

The correct option is A) 318 K.

To convert temperature from Fahrenheit to Kelvin, one must first convert from Fahrenheit to Celsius and then from Celsius to Kelvin.

The formula for converting Fahrenheit (T_F) to Celsius (T_C) is T_C = (T_F – 32) * 5/9.
Given T_F = 113 °F, T_C = (113 – 32) * 5/9 = 81 * 5/9 = 9 * 5 = 45 °C.
The formula for converting Celsius (T_C) to Kelvin (T_K) is T_K = T_C + 273.15. For practical purposes in MCQs, 273 is often used.
Using 273: T_K = 45 + 273 = 318 K.
Using 273.15: T_K = 45 + 273.15 = 318.15 K.
Since 318 K is an option and close to 318.15 K, it is the intended answer using the approximation of 273.

10 g of ice at $-10^\circ$C is mixed with 10 g of water at $0^\circ$C. The amount of heat required to raise the temperature of mixture to $10^\circ$C is

[amp_mcq option1=”400 cal” option2=”550 cal” option3=”1050 cal” option4=”1200 cal” correct=”option3″]

To calculate the total heat required, we need to consider the heat needed for each stage of the process:
1. Heat required to raise the temperature of 10 g of ice from -10°C to 0°C:
$Q_1 = m_{ice} \times c_{ice} \times \Delta T_1$
Assuming specific heat of ice $c_{ice} = 0.5 \, \text{cal/g}^\circ\text{C}$.
$Q_1 = 10 \, \text{g} \times 0.5 \, \text{cal/g}^\circ\text{C} \times (0^\circ\text{C} – (-10^\circ\text{C})) = 10 \times 0.5 \times 10 = 50 \, \text{cal}$.
2. Heat required to melt 10 g of ice at 0°C into water at 0°C:
$Q_2 = m_{ice} \times L_{fusion}$
Assuming latent heat of fusion of ice $L_{fusion} = 80 \, \text{cal/g}$.
$Q_2 = 10 \, \text{g} \times 80 \, \text{cal/g} = 800 \, \text{cal}$.
After this step, we have 10 g of water at 0°C.
3. Heat required to raise the temperature of the 10 g of water (from melted ice) from 0°C to 10°C:
$Q_3 = m_{water(ice)} \times c_{water} \times \Delta T_2$
Assuming specific heat of water $c_{water} = 1 \, \text{cal/g}^\circ\text{C}$.
$Q_3 = 10 \, \text{g} \times 1 \, \text{cal/g}^\circ\text{C} \times (10^\circ\text{C} – 0^\circ\text{C}) = 10 \times 1 \times 10 = 100 \, \text{cal}$.
4. Heat required to raise the temperature of the initial 10 g of water from 0°C to 10°C:
$Q_4 = m_{water(initial)} \times c_{water} \times \Delta T_3$
$Q_4 = 10 \, \text{g} \times 1 \, \text{cal/g}^\circ\text{C} \times (10^\circ\text{C} – 0^\circ\text{C}) = 10 \times 1 \times 10 = 100 \, \text{cal}$.

Total heat required = $Q_1 + Q_2 + Q_3 + Q_4 = 50 + 800 + 100 + 100 = 1050 \, \text{cal}$.

– Heat transfer during phase change (melting or freezing) involves latent heat ($Q = mL$).
– Heat transfer during temperature change involves specific heat ($Q = mc\Delta T$).
– Need to account for heat required for each component (ice and water) and each process (heating ice, melting ice, heating water).

The problem assumes standard values for specific heat capacities of ice and water and the latent heat of fusion of ice. If the final temperature was, for example, 0°C, we would first check if the initial water had enough heat to raise the ice to 0°C and then melt it completely. In this case, the target temperature is above 0°C, implying all ice must first melt.

If the work done on the system or by the system is zero, which one of the following statements for a gas kept at a certain temperature is correct ?

[amp_mcq option1=”Change in internal energy of the system is equal to flow of heat in or out of the system.” option2=”Change in internal energy of the system is less than heat transferred.” option3=”Change in internal energy of the system is more than the heat flow.” option4=”Cannot be determined.” correct=”option1″]

The first law of thermodynamics states that the change in internal energy of a system ($\Delta U$) is equal to the heat added to the system ($Q$) minus the work done by the system ($W$). This can be written as $\Delta U = Q – W$. The question states that the work done on the system or by the system is zero, meaning $W = 0$. Substituting this into the first law equation gives $\Delta U = Q – 0$, which simplifies to $\Delta U = Q$. Therefore, the change in internal energy of the system is equal to the flow of heat in or out of the system.

– First Law of Thermodynamics: $\Delta U = Q – W$.
– Work done is zero ($W=0$).
– The change in internal energy is directly equal to the heat transfer when no work is done.

This condition ($W=0$) occurs in processes where the volume of the system does not change (isochoric process) or when the system is rigid. Heat flowing into the system increases its internal energy ($Q > 0, \Delta U > 0$), and heat flowing out decreases its internal energy ($Q < 0, \Delta U < 0$).

Which one of the following statements is correct?

[amp_mcq option1=”Both boiling and evaporation are surface phenomena.” option2=”Boiling is a surface phenomenon, but evaporation is a bulk phenomenon.” option3=”Both boiling and evaporation are bulk phenomena.” option4=”Boiling is a bulk phenomenon, but evaporation is a surface phenomenon.” correct=”option4″]

The correct option is D) Boiling is a bulk phenomenon, but evaporation is a surface phenomenon.

Evaporation is the process where molecules at the surface of a liquid gain enough kinetic energy to overcome the intermolecular forces and escape into the gaseous phase. This occurs at any temperature below the boiling point and only happens at the liquid’s surface.
Boiling is the process where a liquid turns into a vapor when its vapor pressure equals the surrounding atmospheric pressure. This occurs at a specific temperature (the boiling point) and involves the formation of vapor bubbles *throughout* the volume (bulk) of the liquid, which then rise to the surface. It is a phenomenon that occurs throughout the bulk of the liquid, not just at the surface.

Think of boiling water: bubbles form at the bottom and rise. Think of a puddle drying up: the surface reduces as water evaporates. Sublimation is another phase transition, from solid directly to gas, and it is typically a surface phenomenon. Melting is a bulk phenomenon.

In which of the following phenomena do heat waves travel along a straight line with the speed of light ?

[amp_mcq option1=”Thermal conduction” option2=”Thermal convection” option3=”Thermal radiation” option4=”Both, thermal conduction and radiation” correct=”option3″]

The correct option is C) Thermal radiation. Heat transfer by radiation involves electromagnetic waves, which travel at the speed of light.

Heat can be transferred by conduction, convection, and radiation. Conduction is the transfer of heat through direct contact via vibrations of particles. Convection is the transfer of heat through the movement of fluids (liquids or gases). Both conduction and convection require a medium and the speed of heat transfer is much slower than the speed of light. Radiation is the transfer of heat through electromagnetic waves, such as infrared radiation. These waves can travel through a vacuum and propagate at the speed of light (approximately 3 x 10⁸ m/s in vacuum).

Heat from the Sun reaches the Earth primarily through radiation, traveling across the vacuum of space at the speed of light. Conduction is how a metal spoon gets hot when placed in hot soup. Convection is how water heats up in a pot or how air circulates in a room.

The coefficient of areal expansion of a material is 1•6×10⁻⁵ K⁻¹. Which one of the following gives the value of coefficient of volume expansion of this material?

[amp_mcq option1=”0•8×10⁻⁵ K⁻¹” option2=”2•4×10⁻⁵ K⁻¹” option3=”3•2×10⁻⁵ K⁻¹” option4=”4•8×10⁻⁵ K⁻¹” correct=”option2″]

The value of the coefficient of volume expansion of this material is 2.4×10⁻⁵ K⁻¹.

– For an isotropic solid material, the coefficients of linear expansion (α), areal expansion (β), and volume expansion (γ) are related.
– The relationship is approximately β ≈ 2α and γ ≈ 3α.
– From these relations, we can derive the relationship between the coefficient of areal expansion (β) and the coefficient of volume expansion (γ): γ = (3/2)β.
– Given coefficient of areal expansion β = 1.6 × 10⁻⁵ K⁻¹.
– Substitute the value into the formula: γ = (3/2) * (1.6 × 10⁻⁵ K⁻¹).
– γ = 1.5 * 1.6 × 10⁻⁵ K⁻¹ = 2.4 × 10⁻⁵ K⁻¹.

– These relationships (β=2α, γ=3α) are valid for small changes in temperature and for isotropic materials (materials with the same properties in all directions).
– Linear expansion refers to the change in length, areal expansion to the change in area, and volume expansion to the change in volume per unit change in temperature.