CALORIMETRY

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).

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

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).

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

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 solid by an electrical method

Specific Heat Capacity of a liquid by an electrical method

• 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 liquidcC specific heat capacity of container

• Equating the two quantities,

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

• 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.

where,mS - mass of solidcS - specific heat capacity of solid mS is known and V, I, t, Δθ are measured. So the specific heat capacity of the solid (cS)can be calculated.

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:

• 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. Note that 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.

Specific Latent Heat Capacity • 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:

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

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.

• The specific latent heat of ice by the 'method of mixtures'

• 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.

• where,• mL mass of water

mI mass of icemC mass of calorimeter

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

•θhigh temperature of the hot waterθfinal temperature of mixture

•l specific latent heat of fusion of ice

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

The specific latent heat of vaporization of a liquid

• 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

• 3 (a) The resistance of a thermistor at 0 °C is 3840 Ω. At 100 °C the resistance is 190 Ω.

• When the thermistor is placed in water at a particular constant temperature, its resistance is 2300 Ω.

• (i) Assuming that the resistance of the thermistor varies linearly with temperature, calculate the temperature of the water.

• (ii) The temperature of the water, as measured on the thermodynamic scale of temperature, is 286 K.

• By reference to what is meant by the thermodynamic scale of temperature, comment on your answer in (i).

• (b) A polystyrene cup contains a mass of 95 g of water at 28 °C.A cube of ice of mass 12 g is put into the water. Initially, the ice is at 0 °C. The water, of specific heat capacity 4.2 × 103 J kg–1 K–1, is stirred until all the ice melts. Assuming that the cup has negligible mass and that there is no heat exchange with the atmosphere, calculate the final temperature of the water.

• The specific latent heat of fusion of ice is 3.3 × 105 J kg–1.

• (a) Define specific latent heat.• (b) The heater in an electric kettle has a

power of 2.40 kW.When the water in the kettle is boiling at a steady rate, the mass of water evaporated in 2.0 minutes is 106 g. The specific latent heat of vaporisation of water is 2260 J g–1.

• Calculate the rate of loss of thermal energy to the surroundings of the kettle during the boiling process.

• (a) State what is meant by the internal energy of a system.State and explain qualitatively the change, if any, in the internal energy of the following systems:

• (i) a lump of ice at 0 °C melts to form liquid water at 0 °C,

• (ii) a cylinder containing gas at constant volume is in sunlight so that its temperature rises from 25 °C to 35 °C.

• A microwave cooker uses electromagnetic waves of frequency 2450 MHz. The micro waves warm the food in the cooker by causing water molecules in the food to oscillate with a large amplitude at the frequency of the microwaves.

• (a) State the name given to this phenomenon.• The effective microwave power of the cooker is 750 W.• (b) The temperature of a mass of 280 g of water rises from

25 °C to 98 °C in a time of 2.0 minutes. Calculate a value for the specific heat capacity of the water.

• The value of the specific heat capacity determined from the data in (b) is greater than the accepted value.

• A student gives as the reason for this difference: ‘heat lost to the surroundings’. Suggest, in more detail than that given by the student, a possible reason for the difference.