IEMDaily - Video Lecture Notes

Definition

Latent heat of fusion in calorimetric experiment

m_{1}

= mass of the calorimeter and the stirrer

m_{2}

= mass of the water

m_{3}

= mass of the ice

s_{1}

= specific heat capacity of material of the calorimeter and the stirrer

s_{2}

= specific heat capacity of water

θ_{1}

= initial temperature of the water in calorimeter

θ_{2}

= final temperature of the water

L = (m_{1} s_{1} + m_{2} s_{2}) (θ_{1} - θ_{2}) / m_{3} - s_{2} θ_{2}

Example

Mixing of two bodies in same state

If 20g of water at

60^{0} C

is mixed with 60g of water at

20^{0} C

. The resultant temperature isHeat lost by the hot water

=

Heat gained by the cold water

m_{1} c Δ T_{1} = m_{2} c Δ T_{2}

20 (60 - T) = 60 (T - 20)

60 - T = 3 T - 60

4 T = 120

T = 30^{o} C

Example

Mixing of two bodies in different states

5 g of steam at

100^{0} C

is mixed with 5g of the ice at

0^{0} C

. Find the final temperature of the mixture.Latent heat of fusion is

336 J / g

Latent heat of vaporization is

2260 J / g

So, Heat released by

5 g

of steam to condense is

Q_{1} = 5 \times 10^{- 3} \times 2260 \times 10^{3}

and,
Heat absorbed by

5 g

of ice to melt is

Q_{2} = 5 \times 10^{- 3} \times 336 \times 10^{3}

Heat require to increase temperature from

0^{o} C t o 100^{o} C

Q_{3} = m c Δ T = 5 \times 10^{- 3} \times 4200 \times 100 = 2100 J

As,

Q_{1} > Q_{2} + Q_{3}

hence final temperature is at

100^{o} C

.
Partial steam will condense.

Law

Principle of calorimetry

The principle of calorimetry (or principle of mixtures) states that for an insulated system, heat energy lost by the hot body is equal to the heat energy gained by the cold body.

m_{1} c_{1} (t_{1} - t) = m_{2} c_{2} (t - t_{2})

Note: Heat transfer occurs until both the bodies attain the same temperature(

t

Definition

Heat capacity equation

Q = m s Δ θ

where

θ

is the change in temperature,

m

is the mass of the body,

Q

is the heat supplied, and s is a constant for the given material under the given surrounding conditions called the specific heat capacity of the material.
The quantity

m s

is called the heat capacity of the material.

Definition

Describe the principle of method of mixtures

If two or more bodies at different temperatures are brought into thermal contact, the net heat is lost by the hot bodies is equal to net heat gained by the cold bodies until they attain thermal equilibrium. If heat is not lost by any other process to the surroundings,
i.e. Net heat lost= Net heat gain
This is called principle of method of mixtures.

Example

Heat lost to surroundings

A large paraffin candle has a mass of 96.83 gram. A metal cup with 100.0 mL of water at 16.2

^{o}

C absorbs the heat from the burning candle and increases its temperature to 35.7

^{o}

C. Once the burning is ceased, the temperature of the water was 35.7

^{o}

C and the paraffin had a mass of 96.14 gram. Determine the heat of combustion of paraffin in kJ/gram. GIVEN: density of water = 1.0 g/mL.

As is always the case, calorimetry is based on the assumption that all the heat lost by the system is gained by the surroundings. It is assumed that the surroundings is the water that undergoes the temperature change. In equation form, it could be stated that

Q_{p a r a f f i n} = - Q_{w a t e r}

Since the mass and temperature change of the water are known, the energy gained by the water in the calorimeter can be determined.

Q_{w a t e r} = m C Δ T = (100.0 g) (4.18 J / g /^{o} C) ({35.7}^{o} C - {16.2}^{o} C) = 8151 J

The paraffin released 8151 J or 8.151 kJ of energy when burned. This is based on the burning of 0.69 gram (96.83 g - 96.14 g).

Example

Heat transfer using principle of calorimetry

Water of mass

m_{2} = 1 k g

is contained in a copper calorimeter of mass

m_{1} = 1 k g

. Their common temperature is

t = 10^{\circ} C

. Now a piece of ice of mass

m_{3} = 2 k g

and temperature

- 11^{\circ} C

is dropped into the calorimeter. Neglecting any heat loss, find the final temperature of the system. (specific heat of copper

0.1 K c a l / k g^{\circ} C

, specific heat of water

= 1 K c a l / k g^{\circ} C

, specific heat of ice

= 0.5 K c a l / k g^{\circ} C

, latent heat of fusion of ice

= 78.7 K c a l / k g

)Heat is lost by calorimeter plus water while it is gained by ice.
Heat lost = heat gained

Q_{l o s t} = Q_{c a l o r i m e t e r} + Q_{w a t e r}

= m_{c a l o r i m e t e r} \times s_{c a l o r i m e t e r} \times (10 - 0) + m_{w a t e r} \times s_{w a t e r} \times 10

= 1 \times 1 \times 10 + 1 \times 0.1 \times 10

= 11 k c a l

Q_{g a i n e d} = m_{i c e} \times s_{i c e} \times (0 - (- 11)) = 2 \times 0.5 \times 11 = 11 k c a l

Thus, all the heat lost by calorie meter and water is used for melting the ice from

- 11^{0} C

0^{0} C

.
Hence, the final temp of the system will be

0^{0} C

, ice and water will co-exist at

0^{0} C

Definition

Setup for measurement of latent heat of vaporization

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.

Example

Experimental verififcation of water as a bad conductor of heat

Take a test tube filed with water. Now put a piece of ice wrapped with a wire in the test tube. The piece of ice will sink to the bottom of the test tube because of the weight of the wire. Now heat the water at the top end of the test tube over a burner. You will see that the water at the top starts boiling while the ice at the bottom of the tube has still not melted. This implies that the heat supplied at the top is not conducted well to the bottom to melt the ice.

Definition

Regnault's apparatus

The experimental solid is weighed and suspended in the steam chamber O kept on a wooden platform D. The upper part of the vessel is closed by a cork and a thermometer

T_{1}

is also placed inside the vessel to measure the temperature of the solid. Steam is passed through A. A wooden partition P separates the steam chamber from the calorimeter C. The calorimeter with a stirrer is weighed and sufficient amount of water is kept to completely immerse the solid. The calorimeter with water is again measured. The initial temperature of the water is noted.
When the temperature of the solid is constant after some time, the partition P is removed, the calorimeter is taken below the steam chamber, the wooden disc D is removed and the thread is cut to drop the solid in the calorimeter. The calorimeter is taken to its original place and stirred. The maximum temperature of the mixture is noted.

Definition

Experimental measurement of specific heat capacity

Regnaults apparatus is used to determine the specific heat capacity of solids heavier than water and insoluble in it.Calculation of specific heat from observations: