CBSE Class 12 Physics Calorimetry Theory and Examples

CBSE Class 12 Physics Calorimetry Theory and Examples. Please refer to the examination notes which you can use for preparing and revising for exams. These notes will help you to revise the concepts quickly and get good marks.

Calorimetry is that branch of heat which deals with its measurement. the useual units of heat are calorie or kilocalorie

1. SPECIFIC HEAT
This is also called ' Heat Inertia' of a substance

1.1 Specific Heat of solid & Liquid (s) : If a solid or a liquid is heated till the change of the state, there is no change in their volume hence the work done is zero. Hence there is only one specific heat of solids and liquids which is constant.
1. Definition : The amount of heat needed for an unit increase in the temperature of unit mass of a solid or liquid is called it's specific heat Unit : kilocalorie / kg-ºC or calorie/g-ºC

1 Kcal / Kg-ºC = 1 Cal/g-ºC

2. If mass of the body is 'm' and specific heat is 's' then amount of heat needed to increases it's temperature by dT is given by Q = msdT

3. Specific heat of water = 1 kcal / kg-ºC = 1
Cal/ g-ºC = 4.18 × 103 J/kg-ºC

4. Kelvin can also be used instead of ºC is size of both uints is same.

1.2 Specific heat of gas (C)

(1) There are many processes possible to give heat to a gas. A specific heat can be associated to each such process which depends on the nature of process.

(2) The number of possible specific heats for a gas is infinite and the value of specific heats can very from zero (0) to infinity (∞).

(3) Generally two types of specific heat are mentioned for a gas -
(a) specific heat at constant volume (Cv)
(b) specific heat at constant pressure (Cp)

(4) These specific heats can be molar or gram, depending on the amount of gas considered to define it

(5) The molar heat capacities of a gas are defined as the heat given per mole of the gas per unit rise in the temperature

(6) The molar heat capacity at constant volume, denoted by Cv is Cv = (ΔQ/nΔT)

(7) If, at absolute temperature T , total energy of a gas E , degree of freedom of gas = f

⇒ E =2fRT and Cv =ΔE/ΔT

⇒ CV =Rf/2

(8) Amount of heat needed to increase the temperature of n moles of gas by dT at constant volume is
dθ = nc_v dT.

(9) Amount of heat needed to increase the temperature of 1gm of gas by 10C at constant volume is called gram specific heat at constant volume.

(10) (C_v)gram =M(C_v )molar  or (C_v)molar = M(C_v)gram
where M = molecules wt . of gas

(11) Amount of heat needed to increases temperature of 'm' gm of gas by dT at constant volume is
dQ = m (C_v) gram dT =m/M (C_v)molar dT

(12) Amount of heat needed to increase temperature of 1mole of gas by 10C at constant pressure is called molar specific heat at constant pressure.

(13) Cp = Cv + R, for one mole. where R = universal gas constant

(14) Amount of heat needed to increase temperature of n moles of gas by dT is at constant pressure
dQ = nC_p dT
Note : If gas is heated at constant pressure, then Cv can be replaced by Cp in above discussion. Hence
(a) (C_p)gram =C_P/M or C_p = M (C_p)gram

(15) Specific heat for other processes  (S=Q/mΔT)

(a) adiabatic s = 0, as Q = 0 but ΔT has some value
(b) isothermal s = ∞ , as ΔT = 0 but Q has some value

(16) Specific heat for any process is given by C = C_v + pdV/ndT = Cp – R + pdV/ndT
(for the n mole of gas)

Example :
(1) If process is isochoric , then dV = 0
⇒ C = C_v
(2) If process is isobaric , then pV = nRT
⇒pdV/ dT = nR
⇒ C = Cv + R = Cp (for one mole)

2 THERMAL CAPACITY
(1) Amount of heat needed to increase the temperature of a substance (any amount) by 1ºC is called thermal capacity of that substance.

(2) Thermal capacity = ( mass of body ) x (specific heat) ⇒ Hc = ms

(3) Unit = calorie /ºCor Kcal/ºC Heat capacity at point 'p' = 1/ tan θ = cotθ

(4) Thermal capacity is given by reciprocal of slope of heat temperature curve.as H_c = mS = Q/dT

(5) Heat capacity in an isothermal process is infinite (∞). e.g. process of melting and vaporisation

(6) If heat capacity of a body is Hc, then heat needed to rise it's temperature by dθ is, dQ = H_c dθ

3. WATER EQUIVALENT OF A BODY

(1) If m gram of a substance is given Q amount of heat which rises its temperature by ΔT . Now if on giving same amount of heat temperature of w gram of water is also increased by ΔT then w is called water equivalent of body of mass m.

(2) The value of water equivalent of a body is same as it's heat capacity. The difference is only in units. e.g If heat capacity of a body is m calorie/ 0C then it's water equivalent will be m gram.

(3) Physical meaning : The same amount of heat has to be given to a body for increasing it'stemperature by dT as needed for quantity of water equal to it's water equivalent by same temperature range.

4. LATENT HEAT

Latent heat of fusion of a substance is the quantity of heat (in kilocalories) required to change its 1 kg mass from solid to liquid state at its melting point (For ice latent heat of fusion = 80 kilocal/kg). Latent heat of vaporization of a substnce is the quantity of heat required to change its 1 kg mass from liquid to vapour state at its boiling point. For water latent heat of vaporisation = 536 kilocal/kg

Specific heat, thermal capacity & latent heat

Ex.1 The amount of heat necessary to raise the temperature of 0.2 mol of N2 at constant pressure from 37º to 337º C will be -
(A) 1764 Joule (B) 764 Joule
(C) 1764 Calorie (D) 1764 erg
Sol.[A] dQ = nCPdT
dQ = 0.2 × 7 × 300
dQ = 420 Calorie
∴ dW = 420 × 4.2
dW = 1764 Joule

Ex.2 (Cp – Cv) will be -
(A) Maximum for oxygen
(B) Maximum for nitrogen
(C) Maximum for carbon di oxide
(D) Same for all gases
Sol.[D] (C_p – C_v) = R, where R is gas constant which is same for all gases. So (C_p – C_v) is same for all gases.

Ex.3 The ratio of radii of two copper spheres is 2 : 1 and they are kept at same temperature. The ratio of their heat capacities will be -
(A) 2 : 1 (B) 1 : 1
(C) 8 : 1 (D) 4 : 1
Sol.[C] dQ₁/dQ₂=4/3∏r³₁ΡS/4 /3∏r³₂ΡS = r1/r2 ³= 2/1 ³ =8/1 

Ex.4 5 g of ice at 0°C is dropped ina beaker containing 20 g of water at 40°C, then
(A) All the ice will not melt into water
(B) All the ice will melt and the resulting temperature of water will be 0°C
(C) All the ice will melt and the resulting temperature of water will be 25°C
(D) All the ice will melt and the resulting temperature of water will be 16°C

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