Solution - Career Point

PHYSICS FUNDAMENTAL FOR IIT-JEECalorimetry, K.T.G., Heat transferKEY CONCEPTS & PROBLEM SOLVING STRATEGYCalorimetry :The specific heat capacity of a material is the amountof heat required to raise the temperature of 1 kg of itby 1 K. This leads to the relationQ = ms θwhere Q = heat supplied, m = mass, θ = rise intemperature.The relative specific heat capacity of a material is theratio of its specific heat capacity to the specific heatcapacity of water (4200 J kg –1 K –1 ).Heat capacity or thermal capacity of a body is theamount of heat required to raise its temperature by 1K. [Unit : J K –1 ]Thus heat capacity = Q/θ = msdθ 1 dQAlso = ×dt ms dti.e., the rate of heating (or cooling) of a body dependsinversely on its heat capacity.The water equivalent of a body is that mass of waterwhich has the same heat capacity as the body itself.[Unit : g or kg] This is given bym×sW =s wwhere m = mass of body, s = specific heat capacity ofthe body, s w = specific heat capacity of water.Principle of Calorimetry : The heat lost by onesystem = the heat gained by another system. Or, thenet heat lost or gainsed by an isolated system is zero.It system with masses m 1 , m 2 , ...., specific heatcapacities s 1 , s 2 , ...., and initial temperatures θ 1 , θ 2 , ....are mixed and attain an equilibrium temperature θthenθ =Σmsθ, for equal masses θ =Σms´ΣsθΣsNewton's law of cooling :The rate of loss of heat from a body in anenvironment of constant temperature is proportionalto the difference between its temperature and that ofthe surroundings.If θ = temperature of the surroundings thendθ– ms = C´(θ – θ0 )dtwhere C´ is a constant that depends on the nature andextent of the surface exposed. Simplifyingdθ C= –C(θ – θ0 ) where C = = constantdtmśKinetic theory of gases :The pressure of an ideal gas is given by p = 31 µnC2where µ = mass of each molecule, n = number ofmolecules per unit volume and C is the root squarespeed of molecules.p = 31 ρC2or pV = 31 mC2where ρ is the density of the gas and m = mass of thegas.Root Mean Square Speed of Molecules :This is defined as222C1 + C2+ C3+ ... + CNC =Nwhere N = total number of molecules. It can beobtained through these relationsC =3pρ=3RTMTotal Energy of an ideal gas (E) :This is equal to the sum of the kinetic energies of allthe molecules. It is assumed that the molecules do nothave any potential energy. This follows from theassumption that these molecules do not exert anyforce on each other.1E = mC 2 3 m 3= RT = pV2 2 M 2Thus, the energy per unit mass of gas = 21 C2The energy per unit volume = 23 pThe energy per mole = 23 pV = 23 RT2XtraEdge for IIT-JEE 23 APRIL 2010