Maharashtra State Board · Class 10 · Physics · Chapter 5

Heat — Formula Sheet

Board Formulas

14 formulas

1.Units of Heat
$1 cal = 4.18 J, 1 kcal = 1000 cal$
1 calorie is the heat needed to raise the temperature of 1 g of water by 1 °C (from 14.5 °C to 15.5 °C). The SI unit of heat is the joule (J).
2.Heat Absorbed or Given Out★
$Q = m c Δ T$
$Q$ : 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)
Heat needed to change the temperature of a body without a change of state. ΔT is the change in temperature (°C or K — same number).
3.Specific Heat Capacity
$c = \frac{Q}{m Δ T}$
$c$ : Specific heat capacity (cal/g °C; SI: J/kg °C)
Heat needed to raise the temperature of unit mass of a substance by 1 °C. Water has c = 1 cal/g °C, one of the highest of common substances — which is why it is used in hot-water bags and as a coolant.
4.Principle of Heat Exchange★
$Heat lost by hot body = Heat gained by cold body$
Holds when the two bodies are in contact, no heat is lost to the surroundings, and heat flows until both reach the same temperature.
5.Heat Exchange Equation
$m_{1} c_{1} (T_{1} - T) = m_{2} c_{2} (T - T_{2})$
$m_{1}, c_{1}, T_{1}$ : 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)
Hot body at T₁, cold body at T₂, common final temperature T. Write each bracket as (higher − lower) so that both sides are positive.
6.Final Temperature of a Mixture
$T = \frac{m _{1} c _{1} T _{1} + m _{2} c _{2} T _{2}}{m _{1} c _{1} + m _{2} c _{2}}$
Rearranged form of the heat exchange equation. Valid only if neither body changes state. For two samples of water, c cancels: T = (m₁T₁ + m₂T₂)/(m₁ + m₂).
7.Method of Mixtures with a Calorimeter
$m c (T_{1} - T) = (m_{w} c_{w} + m_{c} c_{c}) (T - T_{2})$
$m, c, T_{1}$ : 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
To find the specific heat c of a solid: the hot solid gives heat to both the water and the calorimeter. Ignore the calorimeter term only if the question says so.
8.Latent Heat★
$Q = m L$
$Q$ : 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)
Heat absorbed or given out during a change of state at constant temperature. Specific latent heat L is the heat needed to change the state of unit mass.
9.Specific Latent Heats of Water
$L_{fusion of ice} = 80 cal/g, L_{vaporisation of water} = 540 cal/g$
In SI units the textbook table gives 333 kJ/kg (3.33 × 10⁵ J/kg) and 2256 kJ/kg (2.256 × 10⁶ J/kg). The same heat is released when water freezes at 0 °C or steam condenses at 100 °C.
10.Heat for a Change through Two States
$Q_{total} = m c_{ice} Δ T_{1} + m L_{f} + m c_{w} Δ T_{2} + m L_{v}$
Ice below 0 °C to steam at 100 °C: warm the ice, melt it, warm the water, boil it. Add the heat for each stage separately. c of ice is not in the textbook table; use the value given in the question (typically 0.5 cal/g °C).
11.Anomalous Behaviour of Water
$ρ_{water} is maximum at 4^{\circ} C$
From 0 °C to 4 °C water CONTRACTS on heating; above 4 °C it expands like other liquids. So water at 4 °C sinks to the bottom of lakes and aquatic life survives under the ice.
12.Absolute Humidity
$Absolute humidity = \frac{mass of water vapour}{volume of air}$
Mass of water vapour present in unit volume of air. Unit: kg/m³ (often quoted in g/m³).
13.Relative Humidity★
$R H = \frac{actual mass of vapour in a given volume}{mass of vapour needed to saturate that volume} \times 100%$
Compare at the SAME temperature. RH has no unit; it is a percentage. When the air is cooled to its dew point, it becomes saturated and RH = 100%.
14.Dew Point
$At the dew point: air is saturated, R H = 100%$
The temperature at which the water vapour in air becomes saturated. Cooling below it makes vapour condense as dew, fog or mist.