Important Calorimetry & Heat Transfer Formulas for JEE and NEET

1. Calorimetry

(i) Q = msΔθ = cΔθ, when temperature changes without change in state.
(ii) Q = mL, when state changes without change in temperature.
(iii) s = specific heat of any substance
= heat required to increase the temperature of unit mass by 1°C or 1 K.
(iv) c = heat capacity of a body = ms
= heat required to increase the temperature of whole body by 1°C or 1 K.
(v) Specific heat of water is 1 cal g^-1 - °C between, 14.5°C and 15.5°C.

(vi) L = latent heat of any substance
= heat required to convert unit mass of that substance from one state to another state.
(vii) Water equivalent of a vessel It is mass of equivalent water which takes same amount of heat as taken by the vessel for same rise of temperature.
2. Heat Transfer
Heat conduction through a rod
(i) Heat flow in steady state
(ii) Rate of flow of heat = heat current or
Here, TD = temperature difference = θ₁ - θ₂ and R = thermal resistance = 1/KA
Radiation
(i) Absorptive power, a=
a ≤ 1
a = 1 for perfectly black body.
(ii) Spectral absorptive power a_l = absorptive power of wavelength l.
a_l ≤ 1
a_l = 1 for perfectly black body.
(iii) Emissive power e Energy radiated per unit area per unit time is called emissive power of a body. Its SI units are Js^-1m^-2 or Wm^-2.
(iv) Spectral emissive power e_l Emissive power of wavelength l is known as spectral emissive power.

(v) Stefan's law Emissive power of a body is given by,
e = e_rσT⁴
Here e_r = emissivity, emittance, relative emissivity or relative emittance.
e_r ≤ 1
e_r = 1 for a perfectly black body.
Sometimes emissivity is also denoted bye. In that case differentiate them by their units. e_r is unitless while e has the units Wm^-2.
(vi) Total energy radiated by a body,
E = e_rσT⁴ At
Here, A = surface area and t = time.
(vii) a = e_r or absorptivity of a body = its emissivity.
(viii) Kirchhoff s law If different bodies (including a perfectly black body) are kept at same temperatures, then

or

From this law following two conclusions can be drawn.
(a) Good absorbers of a particular wavelengthare also good emitters of same wavelength l.(b) At a given temperature, ratio of q_l and a_l for any body is constant. This ratio is equal to e_l of perfectly black body at that temperature.
(ix) Wien's displacement law


or
λ_mT = Constant
= Wien's constant b Here, b = 2.89 × 10^-3 m-K

Further, area of this graph will give total emissive power which is proportional to T⁴,

(x) Cooling of a body by radiation

(a) Rate of cooling

(b) Newton's law of cooling If temperature difference of a body with atmosphere is small, then rate of cooling µ temperature difference.
(c) If body cools by radiation according to Newton, then temperature of body decreases exponentially.

In the figure,

θ_I = initial temperature of body

θ₀ = temperature of atmosphere.
Temperature at any time t can be written as, θ = θ₀ + (θ_I - θ₀)e^-αt
(d) If body is cooling according to Newton then to find temperature of a body at any time t, we will have to calculate e^-αt. To avoid this, you can use a shortcut approximate formula given below