## Thursday, April 24, 2008

### Concept review Ch. 25 Calorimetry

Heat

Heat is a form of energy.

It is energy in transit whenever temperature differences exist.

Once it is transferred it becomes the internal energy of the receiving body.

Calorie: The amount of heat needed to increase the temperature of 1 g of water from 14.5°C to 15.5°C at a pressure of 1 atm is called 1 calorie.

1 cal = 4.186 joule

Principle of calorimetry

The total heat given by the hot objects equals the total heat received by the cold objects.

Specific heat capacity

Q = ms∆θ

m = mass of the body
s = Specific heat capacity
∆θ = temperature change in celsius

Q = nC∆θ

n = number of moles
C = molar heat capacity
∆θ = temperature change in celsius

Determination of specific heat capacity in laboratory

Regnault’s apparatus is used to determine the specific heat capacity of solids heavier than water and insoluble in it.

Calculation of specific heat from observations

m1 = mass of the solid
m2 = mass of the calorimeter and the stirrer
m3 = mass of the water
s1 = specific heat capacity of the solid
s2 = specific heat capacity of material of the calorimeter and the stirrer
s3 = specific heat capacity of water
θ1 = initial temperature of the solid
θ2 = initial temperature of the calorimeter, stirrer and water
θ = final temperature of the mixture

We get s1 = (m2s2 + m3s3)( θ – θ2)/[m1(θ1 – θ)]

Specific heat capacity of a liquid can also be measured with the Regnault apparatus. Here a solid of known specific heat capacity is taken and the experimental liquid is taken in the calorimeter in place of water.

Specific latent heat of fusion and vaporization

Heat is to be supplied to a body during a phase change [from solid to liquid (melting) and liquid to gas (vaporization)]. During the processes of phase change, melting or vaporization, temperature remains constant. The amount of heat supplied is written as

Q = mL
m = mass of substance
L = specific latent heat of fusion

Specific latent heat of fusion is also called as latent heat of fusion. During vaporization also similar relation holds. But L during vaporization (latent heat of vaporization or specific latent heat of vaporization in this case) is higher than L during melting.

When vapour condenses or liquid solidifies, heat is released to the surrounding by the substance.

As heat is supplied as latent heat, internal energy of a body is larger in liquid phase than in solid phase. Similarly, internal energy of a body is larger in gaseous phase than in liquid phase.

Measurement of specific latent heat of fusion of ice.

A calorie meter if filled with water. A piece of ice is taken and as it is melting, it is dried with a blotting paper and put into the calorimeter. The initial temperature of the water is observed and after all the ice has melted the temperature of the water is taken once again. The weight of the empty calorimeter and weight including water are taken as usual.

Observations:

m1 = mass of the calorimeter and the stirrer
m2 = mass of the water
m3 = mass of the ice
s1 = specific heat capacity of material of the calorimeter and the stirrer
s2 = specific heat capacity of water
θ1 = initial temperature of the water in calorimeter
θ2 = final temperature of the water

L = (m1s1 + m2s2)( θ1 - θ2)/m3 - s2θ2

Measurement of specific latent heat of vaporization of water

The experimental set up helps us to send steam with a measured temperature into a calorimeter with known mass of water. The mass of the steam condensed is equal to the increase in the mass of water in the calorimeter after the steam is sent into it.

Observations:

m1 = mass of the calorimeter and the stirrer
m2 = mass of the water
m3 = mass of the steam condensed
s1 = specific heat capacity of material of the calorimeter and the stirrer
s2 = specific heat capacity of water
θ1 = temperature of the steam
θ2 = initial temperature of the water in calorimeter
θ3 = final temperature of the water in the calorimeter after the condensation of steam

L = (m1s1 + m2s2)( θ3 - θ2)/m3 - s2( θ1 - θ2)

Mechanical equivalent of heat

W = JH

When
W is measured in joule
H is measured in calorie

J is expressed in joule/ calorie = 4.186 joule/calorie

The value of J gives how many joules of mechanical work is needed to raise the temperature of water by 1°C.

Measurement of the mechanical equivalent of heat

Searle’s Cone method is used for it.

There is an outer vessel which is rotated using a spindle and an inner vessel which does not move. As the outer vessel is rotated due to friction heat is generated and the water in the inner vessel absorbs it. The temperature of the water in the inner vessel is observed first and then the outer vessel is rotated till water temperature in the inner vessel increases by 5°C. the number of revolution made by the outer vessel is counted.

Observations

m1 = mass of the water in inner vessel
m2 = mass of the two vessels taken together
M = mass of the pan and weights in it
s1 = specific heat capacity of water
s2 = specific heat capacity of material of the vessels
θ1 = initial temperature of the water in calorimeter
θ2 = final temperature of the water
n = number revolutions of the outer vessel
r = radius of the disc

J = 2 πMgr/(m1s1 + m2s2)( θ2 – θ1)