SureDenHeat Capacities
Heat Capacity
Heat capacity of a system is defined as amount of heat required to raise the temp. of a system through 1° C, & it is denoted by ‘C’ C = (dq/dt) ―(1)
Specific Heat Capacity
It is defined as the amount of heat required to raise the temp. of 1g of the substance through 1° C is the known as specific heat capacity.
Molar Heat Capacity →The amount of heat required to raise the temp. of 1 mole of substance through 1° C is known as molar heat capacity.
Heat capacity are of two types-
(1) Heat capacity at constant volume
(2) Heat capacity at constant pressure.
(1). Heat capacity at constant volume:- is the amount of heat required to increase the temp. of system through 1° at constant volume
dE = dq – PdV
dq = dE + Pdv ---(2)
from (1) & (2)
C = (dE + PdV) / dT ------- (3) low. 0 as V= constant
CV = dE/dT
(2). Heat capacity at constant pressure:-
From equation no- (3)
C = (dE/dT) + (PdV/dT) --------(4)
We know, H = E + PV
Differentiating
(dH/dT)=(dE/dT)+(PdV/dT)(VdP/dT) (P is constant so dP = 0)
From (4) & (5)
CP = (dH/dT) = (dE/dT)(PdV/dT)
PV = nRT ----------ideal Gas Equation
For 1 mole n = 1
PdV = RdT
(PdV/dT) = nR
CP = CV + R
Q.11 0.532g of C6H6 = 0.532/78= 0.00682 mole
T = 353 K ,
ΔE = (-22.3/0.00682) = 3269.845 mol.
Prove That CP - CV = R
H = E + PV ---(1) PV = nRT
n = 1 mol.
H = E + RT PV . RT ---(2)
(dH/dT)= (dE/dT)+( λRT/dT)
CP – CV = R
Hence, proved,
Explain that CP is greater than CV.
CP is heat capacity at constant pressure is always higher than heat capacity at constant volume.
Heat capacity at constant volume i.e. the heat given to a system at constant volume so, no external work is done by the gas. & whole of the heat supplied is used up in increasing the internal energy of the system. But if the same system is heated through 1° at constant pressure, extra amount of heat is needed as same heat energy will be used up in doing some work of expansion, Hence, heat capacity at constant pressure will be greater than heat capacity at constant volume.