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THERMAL PHYSICS

 

Calorimetry

 

heat capacity

specific heat capacity

SHC by experiment.

latent heat

specific latent heat capacity

SLHC by experiment

 

 

 

Heat (thermal) Capacity C

 

Heat capacity (C) is the heat energy required to raise the temperature of a body by

 

one degree (oC or K).

 

heat capacity equation

 

where,

 

ΔQ  is the heat energy added to the body
Δθ  is the temperature rise of the body
C    is the heat capacity of the body

 

The units of heat capacity are Joules per degree.

 

Since Kelvin and Celsius degrees are equivalent the units are: JK-1 or JC-1

 

 

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Specific Heat Capacity c

 

 

Specific heat capacity (c) is the heat energy required to raise the temperature of unit

 

mass by one degree (oC or K).

 

specific heat capacity equation

 

where,

 

ΔQ  is the amount heat energy concerned
m    is the mass of the body
Δθ   is the temperature rise of the body
c      is the specific heat capacity of the body

 

The units of specific heat capacity are Jkg-1K-1 or Jkg-1C-1

 

 

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Determination of Specific Heat Capacity by Experiment

 

These two methods concern the heating up a known mass and measuring the temperature rise for a known amount of electrical energy used.

 

 

Specific Heat Capacity of a Liquid by an Electrical Method

 

 

 

specific heat capacity of a liquid - diagram of apparatus

 

 

 

The heat energy supplied by the electrical element is given to the liquid and its container, producing a temperature rise Δθ.

 

The heater current (I) and voltage (V) are monitored for a time (t).

 

energy supplied by heater = VIt

 

energy absorbed by liquid and container = mLcLΔθ + mCcCΔθ

 

where,

 

mL   mass of liquid
mC   mass of container
cL     specific heat capacity of liquid
cC    specific heat capacity of container

 

 

Equating the two quantities,

 

electrical method for the specific heat capacity of a liquid - equation

 

mL , mC , cC are known and V, I, t, Δθ are all measured.

 

So the specific heat capacity of the liquid (cL)can be calculated.

 

 

 

Specific Heat Capacity of a Solid by an Electrical Method

 

 

specific heat capacity experiment - diagram

 

 

The method is very similar to that for a liquid except that there is no container.

 

The solid under test is a lagged cylinder with holes drilled for the thermometer and the heater element.

 

A little glycerine is added to the thermometer hole to improve thermal contact.

 

Heat energy supplied by the electrical element is given directly to the solid, producing a temperature rise Δθ.

 

experiment determining the specific heat capacity of a solid - equation

 

where,

 

mS - mass of solid
cS  - specific heat capacity of solid

 

mS is known and V, I, t, Δθ are measured.

 

So the specific heat capacity of the solid (c S)can be calculated.

 

 

NB More accurate results can be obtained by applying a 'cooling correction'.
This is based on Newton's Law of Cooling, which states :
The rate of cooling is proportional to the excess temperature over the environment.

 

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Latent Heat

 

Latent heat is the energy involved when a substance changes state.

 

Latent heat energy (L) has two components:

 

ΔU - the increase/decrease in internal PE

ΔW - the external work involved in expansion(+ΔW) and contraction(-ΔW)

 

This can be summarized as:

 

specific latent heat energy equation

 

 

The phase changes involving latent heat energy are:

 

 

phase change

action

symbol

solid to liquid

melting

LF

liquid to solid

fusion

LF

liquid to vapour

vaporization

LV

vapour to liquid

condensation

LV

solid to vapour

sublimation

LS

vapour to solid

sublimation

LS

 

 

The graph illustrates the temperature changes when a solid(eg ice) is heated from below its melting point, to above boiling.

 

 

temperature-time graph of ice melting to vapour

 

 

NB The changes of state occur in the flat areas. There is no temperature rise here and hence no increase in KE.

 

Latent heat must be absorbed from the surroundings (and given to the substance) for the substance to melt or boil.

 

Latent heat is given out to the surroundings (from the substance) when the substance condenses or freezes.

 

 

 

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Specific Latent Heat Capacity l

 

The latent heat of fusion of a substance is the energy involved in changing the state of unit mass of the substance at the melting/freezing point.

 

The latent heat of vaporization of a substance is the energy involved in changing the state of unit mass of the substance at the boiling point.

 

 

This may be summarized by the equation:

 

specific latent heat energy equation #2

 

where,

 

ΔQ  is the amount heat energy concerned
m    is the mass of substance
l      specific latent heat of fusion/vaporization

The units of specific heat capacity are Jkg-1.

 

 

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Determination of Specific Latent Heat Capacity by Experiment

 

There are a number of different methods for finding l  for different substances and different phase changes.

 

 

Here we will briefly look at two methods concerning fusion and vaporization.

 

(1)The Specific Latent Heat of Ice by the 'Method of Mixtures'

 

 

specific latent heat method of mixtures apparatus

 

 

Ice cubes are added to hot water of known temperature in a copper calorimeter.

 

The mixture is stirred until all the ice has melted and a final reading of temperature taken.

 

 

determination of specific latent heat capacity  by the method of mixtures

 

 

method of mixtures equation

 

where,

 

mL   mass of water
mI   mass of ice
mC   mass of calorimeter


cL     specific heat capacity of liquid water
cC    specific heat capacity of calorimeter


θhigh temperature of the hot water
θfinal temperature of mixture


     specific latent heat of fusion of ice

 

 

Hence l can be calculated from the knowns and measured values.

 

 

 

(2)The Specific Latent Heat of Vaporization of a Liquid

 

 

specific latent heat capacity of vaporization - apparatus

 

 

Water is heated electrically until it boils. The condensed water (m) is collected over time (t).

 

Heating element readings of voltage (V) and current (I) are recorded.

 

 

In the steady state,

 

electrical energy supplied = heat energy to produce steam

 

latent heat of vaporization equation

 

 

 

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