Heat and Thermodynamics

51. The time period of a simple pendulum made using a thin copper wire of

The time period of a simple pendulum made using a thin copper wire of length L is T. Suppose the temperature of the room in which this simple pendulum is placed increases by 30°C, what will be the effect on the time period of the pendulum ?

[amp_mcq option1=”T will increase slightly” option2=”T will remain the same” option3=”T will decrease slightly” option4=”T will become more than 2 times” correct=”option1″]

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UPSC NDA-1 – 2017
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The time period of the pendulum, T, will increase slightly.
The time period (T) of a simple pendulum is given by the formula T = 2π * sqrt(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. The length of the pendulum is the length of the wire. Materials expand when heated due to thermal expansion.
When the temperature of the room increases, the copper wire of the simple pendulum will undergo thermal expansion, causing its length L to increase. According to the formula T = 2π * sqrt(L/g), the time period T is directly proportional to the square root of the length L (T ∝ √L). Since the length L increases with the increase in temperature, the time period T will also increase. The thermal expansion for a 30°C temperature change is typically small for common materials like copper, leading to a slight increase in the length and consequently a slight increase in the time period.

52. The amount of heat required to change a liquid to gaseous state withou

The amount of heat required to change a liquid to gaseous state without any change in temperature is known as

[amp_mcq option1=”specific heat capacity” option2=”mechanical equivalent of heat” option3=”latent heat of vaporization” option4=”quenching” correct=”option3″]

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The heat energy required to change the state of a substance from liquid to gas at a constant temperature (its boiling point) is called the latent heat of vaporization. This energy is used to overcome the intermolecular forces holding the substance in the liquid state during the phase change, rather than increasing the kinetic energy of molecules, which would increase temperature.
Latent heat is the heat absorbed or released during a phase transition (like melting, freezing, vaporization, condensation, sublimation) that occurs at a constant temperature. ‘Latent’ means hidden, as the heat transfer does not result in a temperature change during the process.
Specific heat capacity relates heat added to temperature change. Mechanical equivalent of heat relates work and heat. Quenching is a rapid cooling process.

53. Which one of the following statements is NOT correct?

Which one of the following statements is NOT correct?

[amp_mcq option1=”In the conduction mode of transference of heat, the molecules of solid pass heat from one molecule to another without moving from their positions.” option2=”The amount of heat required to raise the temperature of a substance is called its specific heat capacity.” option3=”The process of heat transfer in liquids and gases is through convection mode.” option4=”The process of heat transfer from a body at higher temperature to a body at lower temperature without heating the space between them is known as radiation.” correct=”option2″]

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Statement B is incorrect. The amount of heat required to raise the temperature of *one unit mass* of a substance by one degree Celsius (or Kelvin) is called its specific heat capacity. The amount of heat required to raise the temperature of a substance by one degree Celsius (or Kelvin), without specifying the mass, is called its heat capacity or thermal capacity. Statement A correctly describes conduction in solids, Statement C correctly describes convection as the primary mode of heat transfer in fluids, and Statement D correctly describes radiation as heat transfer via electromagnetic waves not requiring a medium.
Specific heat capacity is an intrinsic property of a material (per unit mass), while heat capacity depends on both the material and its total mass.
Conduction is heat transfer through direct molecular contact and vibrations. Convection is heat transfer through the movement of fluids. Radiation is heat transfer through electromagnetic waves.

54. Which one of the following statements with regard to expansion of mate

Which one of the following statements with regard to expansion of materials due to heating is not correct ?

[amp_mcq option1=”As ice melts, it expands uniformly up to 4°C.” option2=”Mercury thermometer works using the principle of expansion due to heating.” option3=”Small gap is kept between two rails to allow for expansion due to heating.” option4=”The length of metallic wire increases when its temperature is increased.” correct=”option1″]

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The statement “As ice melts, it expands uniformly up to 4°C” is not correct.
Most substances expand when heated, but water exhibits anomalous expansion between 0°C and 4°C. When ice melts at 0°C, it forms liquid water which is denser than ice. As liquid water is heated from 0°C to 4°C, it *contracts* and its density increases, reaching maximum density at 4°C. Only above 4°C does water expand like most other substances when heated. Therefore, the statement that water expands uniformly up to 4°C after melting is incorrect; it contracts from 0°C to 4°C.
Statements B, C, and D are correct applications or observations of thermal expansion. Mercury thermometers work because mercury expands linearly with temperature. Gaps in railway tracks prevent buckling caused by the linear expansion of the rails on hot days. Metallic wires also undergo linear expansion when heated, increasing their length. The anomalous expansion of water is crucial for aquatic life in cold climates, as the densest water (at 4°C) sinks to the bottom, preventing lakes from freezing solid from top to bottom.

55. A glass vessel is filled with water to the rim and a lid is fixed to i

A glass vessel is filled with water to the rim and a lid is fixed to it tightly. Then it is left inside a freezer for hours. What is expected to happen ?

[amp_mcq option1=”The water freezes to ice and the level of ice comes down” option2=”The water in the glass vessel simply freezes to ice” option3=”The glass vessel breaks due to expansion as water freezes to ice” option4=”The water does not freeze at all” correct=”option3″]

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UPSC NDA-1 – 2016
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The correct option is C.
Unlike most substances, water expands when it freezes to form ice. Its volume increases by about 9% upon freezing. If a glass vessel is completely filled with water and tightly sealed, there is no space for this expansion to occur. As the water freezes in the freezer, the expanding ice will exert immense pressure on the rigid glass walls. Glass is brittle and cannot withstand this pressure, causing the vessel to break.
This property of water is why water pipes can burst in freezing weather if they are full and the water freezes inside. It is also why ice floats on water, as the expanded ice is less dense than the liquid water.

56. When a solid is heated, it turns directly into a gas. This process is

When a solid is heated, it turns directly into a gas. This process is called

[amp_mcq option1=”Condensation” option2=”Evaporation” option3=”Sublimation” option4=”Diffusion” correct=”option3″]

This question was previously asked in
UPSC NDA-1 – 2016
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The correct option is C.
The process by which a solid changes directly into a gas upon heating, without passing through the liquid state, is called sublimation. This occurs for substances like dry ice (solid carbon dioxide) and naphthalene.
Condensation is the process of a gas turning into a liquid. Evaporation is the process of a liquid turning into a gas. Diffusion is the movement of particles from a region of higher concentration to a region of lower concentration, typically in gases or liquids.

57. Perspiration cools the body because

Perspiration cools the body because

[amp_mcq option1=”presence of water on the skin is cooling” option2=”evaporation requires latent heat” option3=”water has a high specific heat” option4=”water is a poor conductor of heat” correct=”option2″]

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UPSC NDA-1 – 2015
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Perspiration cools the body through the process of evaporation. When sweat (water) evaporates from the skin surface, it changes from a liquid to a gas. This phase change requires energy, which is absorbed from the skin and underlying tissues. This energy absorbed is known as the latent heat of vaporization. By absorbing heat from the body, the evaporation process effectively cools the skin and helps regulate body temperature.
Evaporation of sweat cools the body because it requires latent heat, which is drawn from the body itself.
Factors like humidity affect the rate of evaporation. In high humidity, evaporation is slower, making it harder for the body to cool down effectively through sweating.

58. A solid is melted and allowed to cool and solidify again. The temperat

A solid is melted and allowed to cool and solidify again. The temperature is measured at equal intervals of time. The graph below shows the change of temperature with time.
[Graph image is part of the question context]
The part of the curve that is practically horizontal is due to

[amp_mcq option1=”latent heat given away by the liquid” option2=”specific heat given away by the liquid” option3=”thermal capacity changes with time keeping temperature constant” option4=”change in density during transformation” correct=”option1″]

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The horizontal part of the cooling curve represents a phase transition. As the liquid cools and reaches its freezing point, it starts to solidify. During the solidification process, the temperature remains constant because the substance is releasing latent heat of fusion (or solidification). This released latent heat compensates for the heat being lost to the surroundings, preventing the temperature from dropping until all the liquid has solidified.
During a phase change (like melting or freezing), the temperature of a pure substance remains constant as latent heat is absorbed or released.
Latent heat is the heat energy absorbed or released by a substance during a phase change at constant temperature. Specific heat is the heat required to raise the temperature of a unit mass of a substance by one degree within a single phase.

59. Statement-I: While putting clothes for drying up, we spread them out.

Statement-I: While putting clothes for drying up, we spread them out.
Statement-II: The rate of evaporation increases with an increase in surface area.

[amp_mcq option1=”Both the statements are individually true and Statement II is the correct explanation of Statement I” option2=”Both the statements are individually true but Statement II is not the correct explanation of Statement I” option3=”Statement I is true but Statement II is false” option4=”Statement I is false but Statement II is true” correct=”option1″]

This question was previously asked in
UPSC NDA-1 – 2015
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The correct option is A. Both statements are individually true, and Statement II is the correct explanation of Statement I.
Statement I is true. Spreading out clothes increases their surface area exposed to the air, which is a common practice to speed up drying.
Statement II is true. Evaporation is a surface phenomenon, where liquid molecules gain enough energy to escape into the gaseous phase from the surface of the liquid. The rate of evaporation is directly proportional to the surface area exposed to the surrounding environment (air). Other factors affecting evaporation rate include temperature, humidity, and wind speed.
By spreading clothes, we maximize the surface area from which water can evaporate, thus increasing the rate of drying. Statement II correctly explains why Statement I is an effective drying method.

60. 100 grams of ice at 0°C is put in 240 grams of water at 5°C. The mixtu

100 grams of ice at 0°C is put in 240 grams of water at 5°C. The mixture finally comes to equilibrium at 0°C with m grams of ice melted in the process. Value of m is close to : (latent heat of ice = 3.33 × 105 J/kg and specific heat of water = 4.2 J g-1°C)

[amp_mcq option1=”0 g” option2=”10 g” option3=”5 g” option4=”15 g” correct=”option4″]

This question was previously asked in
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When the ice at 0°C is put into water at 5°C, the water will lose heat as it cools down to 0°C. This heat is then used to melt the ice at 0°C.
The heat lost by the water is Q_water = m_water * c_water * ΔT_water. Given m_water = 240 g, c_water = 4.2 J g⁻¹°C⁻¹, and ΔT_water = 5°C – 0°C = 5°C. Q_water = (240 g) * (4.2 J g⁻¹°C⁻¹) * (5°C) = 5040 J. This heat melts a mass m of ice. The heat required to melt ice is Q_melt = m * L_f. Given L_f = 3.33 × 10⁵ J/kg = 3.33 × 10⁵ J / 1000 g = 333 J/g.
Setting the heat lost by water equal to the heat gained by the melting ice: 5040 J = m (g) * 333 J/g. m = 5040 / 333 g ≈ 15.135 g. The value of m is closest to 15 g among the given options.
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