The document Important Formulae for Calorimetry and Heat Transfer NEET Notes | EduRev is a part of the JEE Course DC Pandey Solutions for JEE Physics.

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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 = θ_{1} - θ_{2} 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^{-1}m^{-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_{r}σT^{4}

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_{r}σT^{4} 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_{m}T = 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 T^{4},

(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

θ_{0} = temperature of atmosphere.

Temperature at any time t can be written as, θ = θ_{0} + (θ_{I} - θ_{0})e^{-}^{α}^{t}

(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^{-}^{α}^{t}. To avoid this, you can use a shortcut approximate formula given below

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