ASRJC First Law of Thermodynamics

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 1 Additional Notes Section III Thermal Physics Topic 9: First Law of Thermodynamics Content: • Specific heat capacity and specific latent heat • Internal energy • First law of thermodynamics Learning Outcomes: Candidates should be able to: (a) define and use the concepts of specific heat capacity and specific latent heat. (b) show an understanding that internal energy is determined by the state of the system and that it can be expressed as the sum of a random distribution of kinetic and potential energies associated with the molecules of a system. (c) relate a rise in the temperature of a body to an increase in its internal energy. (d) recall and use the first law of thermodynamics expressed in terms of the increase in internal energy, the heat supplied to the system and the work done on the system.

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 2 Additional Notes A.1 What is Specific Heat Capacity • Heating is a process whereby thermal energy is being transferred. • Thermal energy is transferred by conduction, convection or radiation from one body to another due to a temperature difference. • When a body is heated, its temperature rise depends on: 1. its mass - the smaller the mass, the larger the temperature rise for the same amount of heat supplied; 2. the material of which the body is made - objects of the same mass but different materials experience different temperature rise when supplied with the same amount of heat. Th is is determined by a property called the specific heat capacity c of the body. The specific heat capacity c of a substance is the thermal energy per unit mass per unit change in temperature of the substance. where Q = heat supplied m = mass of the substance ∆T = rise in temperature of the substance • SI unit of c is J kg−1 K−1. The heat capacity C of a substance is the thermal energy required per unit change in temperature of the substance. • SI unit of C is J K−1. Qc mT=  Q mc T= A Specific Heat Capacity Δ Δ QC= T Q = C T memorize

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 3 Additional Notes A.2 Practical Uses of Specific Heat Capacity • For a given heat input, if it causes only a small temperature rise in the substance, this means the substance should have a high specific heat capacity. • An example is the use of water as an efficient coolant in a car radiator. The specific heat capacity of water is 4.2  103 J kg−1 K−1 (i.e. 4.2  103 J of energy is required to increase the temperature of 1 kg of water by 1 K). • The table below shows the mean specific heat capacity for some other materials at ordinary temperatures: Mean Specific Heat Capacities / J kg−1 K−1 Aluminium 9.1  102 Ice 2.1  103 Copper 3.9  102 Rubber 1.7  103 Glass (ordinary) 6.7  102 Wood 1.7  103 Iron 4.7  102 Alcohol 2.5  103 Mercury 1.4  102 Glycerine 2.5  103 Lead 1.3  102 Paraffin oil 2.1  103 Worked Example An insulated electric kettle has a 2750 W element, and a heat capacity C of 530 J K−1. 1.7 kg of water is placed in it. Determine how long it will take for the temperature of the water and kettle to rise from 20 oC to 100 oC. State any assumption(s) you have made in your calculations. Specific heat capacity of water c = 4200 J K−1 kg−1 In this topic, the working unit of temperature is the kelvin. When calculating the change in temperature there is no need to convert the unit to the kelvin scale since the change in degree Celsius is the numerically the same as a change in Kelvin Solution Energy supplied = Energy gained by water + Energy gained by kettle Pt = mcT + CT 2750 t = (1.7) (4200) (100-20) + (530) (100-20) t = 223 s Assumption: Negligible thermal energy is lost to the surroundings For relatively small changes in temperature, specific heat capacity c is approximately constant. However, over a wide range of temperature, the value of c for a substance may vary considerably. Unless stated otherwise, specific heat capacity is assumed to be constant.

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 4 Additional Notes Example 1 A copper cube of mass 110 g is heated to a temperature of 100 °C and then rapidly transferred to an insulated aluminum can of mass 80 g containing 200 g of water at 10 °C. Calculate the final steady temperature of the cube and water, assuming that heat loss to the surroundings is negligible. (14 °C) Substance Specific heat capacity Water 4.2  103 J kg-1 K-1 Aluminum 9.1  102 J kg-1 K-1 Copper 390 J kg-1 K-1 Thinking Process What are the energy transfer processes occurring in this system? • The copper will lose energy, while the water and the aluminium can will gain energy. • The final steady temperature is hence lower than 100 °C but higher than 10 °C. What is the implication for the negligible heat loss to the surroundings? • The total energy of the system is conserved. • Hence, the heat loss by the copper is equal to the heat gain by the water and aluminium. Hint: always start by writing a word equation containing all the gains and losses of energy

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 5 Additional Notes • In some situations, supplying (removing) thermal energy to (from) a body does not result in an increase (decrease) in temperature but a phase change takes place. • In the process, the supplied (removed) thermal energy is absorbed (released) as latent heat of vaporization or fusion at a constant temperature. Latent heat, l, of a substance is the thermal energy transferred to change the substance from one phase to another, without any change in temperature. The specific latent heat of fusion, lf, of a substance is the thermal energy per unit mass required to change it from solid to liquid without change of temperature The specific latent heat of vaporisation, lv, of a substance is the thermal energy per unit mass required to change it from liquid to gas without change of temperature. • Thus, if an amount of heat Q is needed to cause a change in state of mass m of a substance, then the specific latent heat l of the substance is given by: • SI unit of l is J kg−1. Example 2 Calculate the heat nee ded to completely vapo rise 200 g of water at a temperature of 30 °C to form steam at a temperature of 100 °C. Specific heat capacity of water = 4200 J kg-1 K-1 Specific latent heat of water = 2260 kJ kg-1 Q m=l Qm= l Thinking Process What are the processes involved here? Energy is absorbed by the water to raise its temperature from 30 °C to 100 °C first. Thereafter, energy is absorbed to vaporise the liquid water into its gaseous state. B Specific Latent Heat memorize memorize The latent heat of vaporization and fusion also refers to the amount of energy released by a substance when it changes from a gas to a liquid, & from a liquid to a solid respectively.

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 6 Additional Notes C.1 What is Internal Energy • Internal energy U of a system is associated with the energy of its constituent par ticles on the microscopic scale, does not include bulk kinetic energy or bulk gravitational potential energy Internal energy is the sum of: 1. the kinetic energy Ek due to the random motion of the atoms / molecules and 2. the potential energy Ep due to intermol