When a system absorbs heat (q), its temperature changes by T.
So, q T
q = C x T
where C is heat capacity which is defined as the amount of heat required to raise the temperature of a substance by 1 oC.
The molar heat capacity of a substance (Cm) is the heat required to raise the temperature of 1 mol of system through 1 oC or 1 K.
The specific heat capacity of a substance (C) is defined as the amount of heat required to raise the temperature of 1 g of substance through 1 oC or 1 K.
q = m x C x T
Relation between Cp and Cv:
Heat capacity at constant pressure = Cp
Heat capacity at constant volume = Cv
The relationship between Cp and Cv is
Cp - Cv = R
The ratio of heat capacities is Poisson's ratio () and it gives an idea about atomicity of gas.
Adiabatic Reversible Process:
For an adiabatic reversible expansion of an ideal gas,
Other relationships are:
where for monoatomic, diatomic and polyatomic gases respectively.
Calorimetry:
Experimental measurement of the energy changes associated with any physical or chemical process is known as calorimetry. Apparatus is called Calorimeter.
Parameters we know:
Parameters we need to determine:
Measurements are made under two different conditions:
•At constant volume
•At constant pressure
At constant volume:
Bomb calorimeter is used to measure heat absorbed at constant volume which ultimately tells about change in internal energy, because at constant volume, U = qv.
Steel vessel which can withstand high pressures. It is immersed in water bath to ensure no heat is lost to surroundings. A stirrer dissipates heat produced in water bath. Combustible substance is burnt in steel bomb. Heat evolved is transferred to water. Thermometer monitors temperature change.
Formula used is q = m x C x T
At constant pressure:
If the bomb calorimeter is operated at constant pressure, i.e. atmospheric pressure, then it tells about the enthalpy of the reaction (rH), because at constant pressure,
rH = qp.
Coffee cup Calorimeter is used to measure ΔH. Styrofoam cup is used as no heat can be exchanged with surroundings. Constant pressure as atmospheric pressure. A stirrer dissipates heat produced in water bath. Reaction takes place in the cup. Heat evolved is transferred to water. Thermometer monitors temperature change.
q = m x C x ΔT
ΔrH = Enthalpy of the reaction
ΔrH = negative, it means that the reaction is exothermic.
ΔrH = positive, it means that the reaction is endothermic.