Is it correct to say: Using mass in kg with c in cal/g °C?

Match the units: grams with cal/g °C, kilograms with J/kg °C (or kcal/kg °C).

Is it correct to say: Using Q = mcΔT for melting ice at 0 °C or boiling water at 100 °C?

During a change of state the temperature stays constant. Use Q = mL for that stage.

Is it correct to say: Writing ΔT as (T − T₁) for the hot body, giving a negative heat?

Write each temperature change as (higher − lower): (T₁ − T) for the hot body and (T − T₂) for the cold one.

Is it correct to say: Saying water is densest at 0 °C?

Water has maximum density at 4 °C. Between 0 °C and 4 °C it contracts on heating — this is the anomalous behaviour.

Is it correct to say: Giving relative humidity a unit such as g/m³?

Absolute humidity has unit kg/m³ (or g/m³). Relative humidity is a ratio of masses, expressed as a percentage with no unit.

Is it correct to say: Confusing heat with temperature?

Heat is energy (cal or J) that flows; temperature (°C or K) tells which way it flows — from higher to lower temperature.

📄 Formula sheet (PDF)

Heat

Latent heat, regelation, anomalous behaviour of water, dew point and humidity, specific heat capacity and the principle of heat exchange — Maharashtra SSC Science-1 Ch 5

📐 14 formulas✏️ 4 examples🎯 6 practice🏫 Maharashtra State Board📚 Class 10✓ 2025–26 syllabus

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Board Exam Tips

→In every mixing problem, write 'Heat lost by hot body = Heat gained by cold body' as the first line, then substitute. It shows the principle and earns a step mark.
→Keep one set of units throughout: grams with cal/g °C, or kilograms with J/kg °C. Mixing g with J/kg °C is a common slip.
→During melting or boiling the temperature does not change, so use Q = mL for that stage, not Q = mcΔT.
→The final temperature of a mixture must lie between the two starting temperatures. Use this to check your answer.
→Be ready to draw Hope's apparatus and the temperature–time graph for water, and to explain why water is densest at 4 °C.

📐 Formulas(14)

Units of Heat

1 cal = 4.18 J, 1 kcal = 1000 cal

Heat Absorbed or Given Out★ Board fav

Q = m c Δ T

Symbol	Meaning
$Q$	Heat absorbed or given out (cal or J)
$m$	Mass (g or kg)
$c$	Specific heat capacity (cal/g °C or J/kg °C)
$Δ T$	Change in temperature (°C)

Specific Heat Capacity

c = \frac{Q}{m Δ T}

Symbol	Meaning
$c$	Specific heat capacity (cal/g °C; SI: J/kg °C)

Principle of Heat Exchange★ Board fav

Heat lost by hot body = Heat gained by cold body

Heat Exchange Equation

m_{1} c_{1} (T_{1} - T) = m_{2} c_{2} (T - T_{2})

Symbol	Meaning
$m_{1}, c_{1}, T_{1}$	Mass, specific heat and initial temperature of the hot body
$m_{2}, c_{2}, T_{2}$	Mass, specific heat and initial temperature of the cold body
$T$	Final common temperature (°C)

Final Temperature of a Mixture

T = \frac{m _{1} c _{1} T _{1} + m _{2} c _{2} T _{2}}{m _{1} c _{1} + m _{2} c _{2}}

Method of Mixtures with a Calorimeter

m c (T_{1} - T) = (m_{w} c_{w} + m_{c} c_{c}) (T - T_{2})

Symbol	Meaning
$m, c, T_{1}$	Mass, specific heat and initial temperature of the hot solid
$m_{w}, c_{w}$	Mass and specific heat of water
$m_{c}, c_{c}$	Mass and specific heat of the calorimeter (with stirrer)
$T_{2}, T$	Initial temperature of water and calorimeter; final temperature

Latent Heat★ Board fav

Q = m L

Symbol	Meaning
$Q$	Heat absorbed during melting/boiling or released during freezing/condensation (cal or J)
$m$	Mass that changes state (g or kg)
$L$	Specific latent heat (cal/g or J/kg)

Specific Latent Heats of Water

L_{fusion of ice} = 80 cal/g, L_{vaporisation of water} = 540 cal/g

Heat for a Change through Two States

Q_{total} = m c_{ice} Δ T_{1} + m L_{f} + m c_{w} Δ T_{2} + m L_{v}

Anomalous Behaviour of Water

ρ_{water} is maximum at 4^{\circ} C

Absolute Humidity

Absolute humidity = \frac{mass of water vapour}{volume of air}

Relative Humidity★ Board fav

R H = \frac{actual mass of vapour in a given volume}{mass of vapour needed to saturate that volume} \times 100%

Dew Point

At the dew point: air is saturated, R H = 100%

✏️ Solved Examples

1Solved Exampleeasy3 steps

How much heat is needed to raise the temperature of 2 kg of water from 25 °C to 75 °C? Give the answer in kcal and in kJ. (c of water = 1 cal/g °C, 1 cal = 4.18 J)

Convert mass to grams to match the units of c.

m = 2 kg = 2000 g, Δ T = 75 - 25 = 5 0^{\circ} C

2Solved Exampleeasy3 steps

200 g of water at 80 °C is mixed with 300 g of water at 20 °C. Assuming no heat is lost to the surroundings, find the final temperature.

Principle of heat exchange, with c the same for both (water).

200 \times 1 \times (80 - T) = 300 \times 1 \times (T - 20)

3Solved Exampleboard3 steps

A 200 g metal block at 100 °C is dropped into 300 g of water at 20 °C. The final temperature is 25 °C. Neglecting heat taken by the container, find the specific heat of the metal. (c of water = 1 cal/g °C)

Heat gained by water.

Q_{w} = 300 \times 1 \times (25 - 20) = 1500 cal

4Solved ExampleHOTS4 steps

50 g of ice at 0 °C is put into 250 g of water at 40 °C. Find the final temperature of the mixture. (L of fusion of ice = 80 cal/g, c of water = 1 cal/g °C)

First check whether all the ice can melt. Heat needed to melt all the ice:

Q_{melt} = 50 \times 80 = 4000 cal

⚠️ Traps & Common Mistakes

⚠️Common Mistakes6

1
Using mass in kg with c in cal/g °C
✓Match the units: grams with cal/g °C, kilograms with J/kg °C (or kcal/kg °C).
2
Using Q = mcΔT for melting ice at 0 °C or boiling water at 100 °C
✓During a change of state the temperature stays constant. Use Q = mL for that stage.
3
Writing ΔT as (T − T₁) for the hot body, giving a negative heat
✓Write each temperature change as (higher − lower): (T₁ − T) for the hot body and (T − T₂) for the cold one.
4
Saying water is densest at 0 °C
✓Water has maximum density at 4 °C. Between 0 °C and 4 °C it contracts on heating — this is the anomalous behaviour.
5
Giving relative humidity a unit such as g/m³
✓Absolute humidity has unit kg/m³ (or g/m³). Relative humidity is a ratio of masses, expressed as a percentage with no unit.
6
Confusing heat with temperature
✓Heat is energy (cal or J) that flows; temperature (°C or K) tells which way it flows — from higher to lower temperature.

🎯 Practice Yourself

🎯Practice Yourself6 questions

Q1
Equal amounts of heat are given to two objects A and B of equal mass. The temperature of A rises by 4 °C and that of B by 6 °C. Which has the greater specific heat, and by what factor?
Q2
How much heat is needed to melt 2 kg of ice at 0 °C completely? (L = 80 cal/g)
Q3
How much heat is released when 50 g of steam at 100 °C condenses to water at 100 °C? (L of vaporisation = 540 cal/g)
Q4
Find the heat needed to convert 100 g of ice at −10 °C into steam at 100 °C. (c of ice = 0.5 cal/g °C, c of water = 1 cal/g °C, L_f = 80 cal/g, L_v = 540 cal/g)
Q5
A room contains 6 g of water vapour per m³ of air. At the room temperature, 15 g per m³ would be needed to saturate the air. Find the relative humidity.
Q6
150 g of water at 70 °C is mixed with 100 g of water at 20 °C. Find the final temperature (no heat loss).

📝 Notes

Heat

Heat is energy that flows from a body at higher temperature to one at lower temperature. This chapter asks two questions: what happens when heat changes the STATE of a substance, and how much heat changes its TEMPERATURE.

Change of state: latent heat

While ice melts at 0 °C or water boils at 100 °C, the thermometer reading stays constant even though heat is being supplied. That heat — the latent heat — is used to change the state, given by $Q = mL$ . For water, $L_f = 80$ cal/g and $L_v = 540$ cal/g.

Regelation: pressure lowers the melting point of ice. Ice under a loaded wire melts, the water flows above the wire and refreezes once the pressure is removed, so the wire passes through the block while it stays whole.

Anomalous behaviour of water

Most liquids contract steadily on cooling. Water contracts only down to 4 °C; from 4 °C to 0 °C it expands. Hope's apparatus shows this: as the water cools, the lower thermometer settles at 4 °C while the upper one falls to 0 °C. Because water is densest at 4 °C, lakes freeze from the top and the water below stays liquid.

Humidity and dew point

Absolute humidity is the mass of vapour per unit volume of air. Relative humidity compares this with the mass needed to saturate the same volume at the same temperature. Cool the air to its dew point and it becomes saturated, so vapour condenses as dew or fog.

Specific heat and heat exchange

$Q = mc\Delta T$ links heat to temperature change. In a mixture, apply the principle of heat exchange: heat lost by the hot body equals heat gained by the cold body. If ice is involved, first check whether all of it can melt, and include the $mL$ term for the stage where the state changes.