Heat Capacity

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Theory

When a system absorbs heat (q), its temperature changes by $âˆ†$ T.

So, q $âˆ âˆ†$ T

q = C x $âˆ†$ 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 (C_m) 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 $âˆ†$ T

Relation between C_p and C_v:

Heat capacity at constant pressure = C_p

Heat capacity at constant volume = C_v

The relationship between Cp and Cv is

C_p - C_v = R

The ratio of heat capacities is Poisson's ratio ( $Î³$ ) and it gives an idea about atomicity of gas.

$Î³ = \frac{C_{p}}{C_{v}}$

Adiabatic Reversible Process:

For an adiabatic reversible expansion of an ideal gas,

$W_{r e v} = \frac{n R}{Î³ - 1} [T_{2} - T_{1}]$

Other relationships are:

$P V^{Î³} = c o n s \tan t$

$T^{Î³} P^{1 - Î³} = c o n s \tan t$

$V^{Î³ - 1} T = c o n s \tan t$

where $Î³ = \frac{5}{3}, \frac{7}{4}, \frac{4}{3}$ 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:

Volume of liquid
Heat capacity of liquid
Heat capacity of calorimeter

Parameters we need to determine:

Heat evolved in the process

Measurements are made under two different conditions:

â€¢At constant volume

â€¢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, $âˆ†$ U = q_v.

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 $âˆ†$ 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 ( $âˆ†$ _rH), because at constant pressure, $âˆ†$ _rH = q_p.

Coffee cup Calorimeter is used to measure Î”H. 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.