Q.100 g of water is supercooled to −10∘C. At this point, due to some disturbance mechanised or otherwise some of it suddenly freezes to ice. What will be the temperature of the resultant mixture and how much mass would freeze? [Sw=1 cal/g/∘C and LFusionw=80 cal/g]
🔒You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.
🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — Latent Heat and Change of State
Latent Heat and Change of State
When a substance changes state — solid to liquid (melting) or liquid to gas (boiling) — it absorbs heat without any change in temperature. The heat that is exchanged during this constant-temperature phase change is called latent heat. For a mass m that completely changes state,
Q=mL,
where L is the specific latent heat of the substance for that transition: the latent heat of fusion Lf for melting/freezing and the latent heat of vaporisation Lv for boiling/condensation. The absorbed energy goes into breaking the bonds between molecules (increasing potential energy) rather than increasing their kinetic energy, which is why the temperature holds steady during the change.
Reading a heating curve. If heat is supplied at a steady rate to ice and the temperature is plotted against time, the graph has sloped segments and flat plateaus:
- A sloped segment (e.g. ice warming, or water warming from 0∘C to 100∘C) is governed by specific heat, Q=mcΔT.
- A horizontal plateau at 0∘C is melting: ice and water coexist in equilibrium while latent heat of fusion is absorbed.
- A horizontal plateau at 100∘C is boiling: water and steam coexist while latent heat of vaporisation is absorbed. …
The key idea is that the supercooled water is unstable. The disturbance triggers freezing, and the latent heat released by the freezing portion warms the entire system to the equilibrium temperature.
- The mixture can only stabilise at 0∘C (the freezing point). Any ice formed will be at 0∘C, and the remaining water will also be at 0∘C. …
Latent heat released by the freezing part warms the whole sample back up to the equilibrium freezing point. The final mixture sits at 0∘C, and 12.5 g of ice forms.
Supercooled water at −10∘C is metastable. Once freezing is triggered, the latent heat released warms the sample. Since ice and water coexist at 0∘C, the temperature rises no further than 0∘C, so the final state is an ice-water mixture at 0∘C.
Using energy conservation for the isolated system: the heat absorbed in warming all 100 g from −10∘C to 0∘C is supplied by the latent heat released when a mass m freezes.
mLFusion=mtotalSwΔT …
Write the energy balance directly as a ratio rather than as two separate 'heat released' / 'heat absorbed' equations: the fraction of water that must freeze is simply Mm=LfSwΔT=801×10=81, so m=8100=12.5 g in one step. Sanity check by limiting cases: if the water were supercooled by only 1°C, almost none would freeze ($m\approx1. …
Showing the 12 most recent of 17 on this concept.
- CBSE 2025Set ANNUAL1 markMCQQ.Triple point of water is (A) 273 K (B) 100 K (C) 273.16 K (D) None of these
›Reveal solutionSolution
The triple point of water is 273.16 K.
The triple point of a substance is the unique combination of temperature and pressure at which its solid, liquid, and gaseous phases can all coexist in thermal equilibrium simultaneously. For water, this occurs at exactly:
Ttr=273.16 K(at a pressure of 4.58 mm of Hg)
…
- CBSE 2025Set ANNUAL1 markMCQQ.The change from solid state to vapour state without passing through the liquid state is called (A) Fusion (B) Regelation (C) Vaporisation (D) Sublimation
›Reveal solutionSolution
The direct solid-to-vapour phase change (without an intermediate liquid state) is called sublimation.
- Fusion: solid → liquid.
- Vaporisation: liquid → gas.
- Regelation: melting under pressure followed by refreezing when pressure is removed (specific to substances like ice). …
- CBSE 2025Set ANNUAL1 markMCQQ.The SI unit of latent heat is (A) joule (B) joule kg^-1 °C^-1 (C) J kg^-1 (D) cal g^-1 °C^-1
›Reveal solutionSolution
The SI unit of latent heat is J kg⁻¹.
Latent heat L is defined by Q=mL, where Q is the heat absorbed or released during a phase change (with no temperature change) and m is the mass undergoing the change:
L=mQ
…
- CBSE 2025Set ANNUAL1 markMCQQ.20 gm ice at 0°C is mixed with 40 gm water at 10°C. Then the resultant temperature will be (A) 0°C (B) +5°C (C) +6.6°C (D) -5°C
›Reveal solutionSolution
The heat available from the warm water is not enough to melt all the ice, so the resultant temperature stays at 0°C.
Heat that could be released by 40 g of water cooling from 10°C to 0°C:
Qreleased=mcΔT=40×1×10=400 cal
Heat required to melt all 20 g of ice at 0°C (latent heat of fusion of ice Lf≈80 cal/g):
Qneeded=mLf=20×80=1600 cal
…
- CBSE 2025Set ANNUAL1 markQ.What is the S.I. unit of latent heat of vaporization?
›Reveal solutionSolution
Latent heat is defined via Q=mL, so its unit is simply energy divided by mass.
Latent heat L is defined by the relation:
Q=mL
where Q is the heat absorbed/released (in joules) during a phase change (here, liquid ↔ vapour) of a mass m (in kg) at constant temperature.
Rearranging: L=Q/m
…
- CBSE 2024Set ANNUAL1 markMCQQ.On increasing the pressure, the melting point of ice (A) increases (B) decreases (C) remains constant (D) none of these
›Reveal solutionSolution
Increasing pressure lowers the melting point of ice.
Most solids expand on melting, and pressure raises their melting point. Ice is an anomaly: it is less dense than the water it melts into (ice contracts as it melts). For such substances, the Clausius-Clapeyron relation predicts the opposite behaviour — increasing external pressure favours the denser …
- CBSE 2024Set ANNUAL1 markMCQQ.The specific latent heat of vaporisation of water is (A) 80 kcal/kg (B) 536 kcal/kg (C) 4.2 kcal/kg (D) 1 kcal/kg
›Reveal solutionSolution
Latent heat of vaporisation of water ≈ 536 kcal/kg (about 22.6×105J/kg).
Latent heat of vaporisation is the amount of heat needed to change 1 kg of a liquid at its boiling point into vapour at the same temperature, with no temperature change during the process. For water at 100°C under normal atmospheric …
- CBSE 2024Set ANNUAL1 markMCQQ.Temperature at which phase transition of matter occurs, depends (A) on volume (B) on pressure (C) on density (D) on mass
›Reveal solutionSolution
The temperature of a phase transition depends on the pressure applied.
A substance's P-T phase diagram shows curves along which solid-liquid, liquid-vapour, and solid-vapour phases coexist. Changing the pressure shifts the temperature at which a given phase boundary is crossed — e.g. water boils below 100°C at reduced (high-altitude) pressure and above …
- CBSE 2024Set SET-AP55001 markQ.The point at which all three states of a substance are in equilibrium is called the ________ point.
›Reveal solutionSolution
The triple point of a substance is the unique combination of temperature and pressure at which its solid, liquid, and gaseous phases all coexist simultaneously in thermodynamic equilibrium.
On a substance's phase diagram (pressure vs temperature), the three phase-boundary curves — fusion (solid-liquid), vaporization (liquid-gas), and sublimation (solid-gas) — meet at exactly one point. At this specific pressure and temperature, all three phases can exist together in a stable, uncha …
- CBSE 2024Set SET-NDP60001 markQ.The boiling point .................... (increases/ decreases) with increase in pressure.
›Reveal solutionSolution
The boiling point of a liquid increases when the external (surrounding) pressure is increased.
A liquid boils at the temperature where its saturated vapour pressure equals the external pressure acting on its surface. If the external pressure is raised (for example, inside a pressure cooker), the liquid must be heated to a higher temperature before its vapour pressure can rise to match this larger external pressure — so the boiling point increases with pressure. This is exactly why food cooks faster in …
- CBSE 2024Set ANNUAL1 markQ.Fill in the blank: The amount of heat required to change the state of any matter is called ______.
›Reveal solutionSolution
Latent heat is the heat absorbed or released during a change of state at constant temperature, without any temperature change.
When a substance changes its physical state (e.g., ice melting to water, or water boiling to steam), heat is absorbed or released, but the temperature of the substance remains constant throughout the change of state. This heat is used entirely to break or form intermolecular bonds, not to raise the temperature. …
- CBSE 2023Set ANN1 markQ.The change of state from liquid to solid is called ________.
›Reveal solutionSolution
When a liquid loses heat and turns into a solid at a fixed temperature (its freezing point), the process is called freezing or solidification.
Matter can exist in solid, liquid, and gaseous states, and it can change from one state to another when heat is added or removed at constant pressure. When a liquid is cooled, its molecules lose kinetic energy; at a particular temperature called the freezing point, the liquid begins to solidify as the molecules settle into a fixed, ordered arrangement. For a pure substance at a given pressure, this happens at a fixed temperature (equal to the melting point of the solid) and the te …
🎓Unlock everything free for 14 days
- ✓Full step-by-step solutions
- ✓Concept-first explanations
- ✓Methods, shortcuts & mistakes
- ✓PYQ mapping + timed mock tests
Full access for 14 days. No credit card required.