First Law of Thermodynamics JPJC Notes

1 JURONG PIONEER JUNIOR COLLEGE 9749 H2 PHYSICS 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 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.

2 Introduction Heat capacity and specific heat capacity allows for the calculation of temperature changes in the interaction between two substances in thermal contact. Latent heat is used to calculate the energy required to change the phase of a substance. Thermodynamics is the study of relationships involving heat, mechanical work, and other aspects of energy and energy transfer. The first law of thermodynamics is central to understanding thermodynamic processes which involve heat and mechanical work. This law extends the principle of conservation of energy in Newtonian mechanics, by introducing the concept of internal energy. 1 Specific Heat Capacity and Specific Latent Heat (a) Candidates should be able to define and use the concepts of specific heat capacity and specific latent heat. 1.1 Heat capacity Heat capacity C of a substance is the amount of thermal energy required to cause a unit rise in temperature of the substance. SI units of heat capacity: J K−1 In symbols, we have QC T=  Hence, Q = C T where Q is the heat supplied (or removed), C is the heat capacity, T is the change in temperature. Note: Heat capacity is dependent on both the mass of the body and the material of the body. Example 1 How much heat must be supplied to an object with a heat capacity of 150 J K−1 in order to increase its temperature from 350 K to 400 K? Solution: We assume that the object does not change phase in this temperature range. Heat supplied = C T = (150)(400 – 350) = 7500 J

3 1.2 Specific heat capacity The specific heat capacity c of a substance is defined as the thermal energy per unit mass required to raise the temperature of the substance by one unit of temperature. SI units of specific heat capacity: J kg−1 K−1 In symbols, we have Qc mT=  Hence, Q = m c T where Q is the heat supplied (or removed), m is the mass of substance, c is the specific heat capacity, T is the change in temperature. Note: The specific heat capacity is the heat capacity per unit mass of a substance and it is characteristic of the material of the substance. Example 2 The heat capacity of 2.0 kg of water is 8400 J K−1. What is the specific heat capacity of water? Solution: Specific heat capacity of water = C / m = 8400 / 2.0 = 4200 J kg−1 K−1 Example 3 An electrical heater supplies 12 00 J of thermal energy to a n aluminium cylinder of mass 32.4 g. What is the increase in temperature of the cylinder? (Specific heat capacity of aluminium = 910 J kg−1 K−1) Solution: We assume that all the h eat supplied by the heater goes into increasing the tem perature of the aluminium cylinder. Heat absorbed by cylinder = m c T 1200 = 0.0324 × 910 × T  T = 40.7 K

4 Example 4 A block of copper of mass 0.50 kg at an initial temperature of 440 K is placed in 0.60 kg of water at 300 K. When thermal equilibrium is attained, the temperature of the system is 310 K. How much heat is lost by the copper block and how much heat is absorbed by the water? Comment on your answers. (Specific heat capacities: water = 4200 J kg−1 K−1, copper = 400 J kg−1 K−1) Solution: Heat change of copper = m c T = 0.50 x 400 x (310 – 440) = – 26000 J = – 26 kJ Since the heat change is negative, heat lost by the copper block is 26 kJ. Heat change of water = 0.60 x 4200 x (310 – 300) = 25200 J = 25 kJ Since the heat change is positive, heat gained by the water is 25 kJ. We see that the heat lost by the copper is greater than the heat gained by the water, which means that some heat (about 1 kJ) was lost to the surroundings (i.e. the air, the container) while the copper block and water were in the process of attaining thermal equilibrium with each other. 1.3 Specific latent heat • There are three phases of matter : solid, liquid and gas . Matter can change from one phase to another. It takes energy for a substance to change from solid to liquid or from liquid to gas. • In using the concept of heat capacity, the substance changes temperature without changing its phase (i.e. it does not go from solid to liquid or from gas to solid). In using the concept of latent heat, the substance changes phase without changing temperature. The heat is termed “latent” because it is present but “hidden” as the temperature stays constant. • Pure substances have sharp melting points and boiling points, as observed in Fig. 1.1. • At these temperatures, when more heat is supplied to the system, the average kinetic energy of the particles does not change (temperature remains constant), and only the potential energy part of the internal energy of the substance increases (particles move further apart from one another). Cu Cu 0.50 kg, 440 K 0.60 kg, 300 K 310 K Fig. 1.1 Phase change with temperature

5 • At the melting point, heat supplied turns the substance from solid into liquid. At the boiling point, heat supplied turns the substance from liquid into gas. If heat is extracted from the substance, the reverse happens; there is solidification or liquefaction without a change in temperature. Specific latent heat l of a substance is the amount of thermal energy per unit mass required to change the phase of the substance at constant temperature. SI units of specific latent heat: J kg−1 In symbols, we have Q = m l where Q is the heat supplied (or removed) to change the phase of the substance, m is the mass of substance, l is the specific latent heat. 1.3.1 Specific latent heat of fusion • In the process of changing from a solid into a liquid, t he rigid molecular structure of the particles in fixed positions breaks down such that the particles can move around one another. • This is known as melting, and the temperature at which this phase change occurs is the melting point of the substance. • The reverse process of forming a solid from the liquid is called freezing or sometimes fusion. Specific latent heat of fusion lf is the amount of thermal energy per unit mass required to convert a solid, at its melting point, into liquid at the same temperature, or vice-versa (from liquid to solid). 1.3.2 Specific latent heat of vaporisation • In the process of changing from a liquid into a gas, t he molecules will move from being next to one another to being very far apart. • This process of going from liquid to gas is known as vaporisation, and the temperature at which this phase change occurs is the boiling point of the substance. • The reverse process of forming a liquid from the gas is called liquefaction. Specific latent heat of vaporisation lv is the amount of thermal energy per unit mass required to convert a liquid, at its boiling point, into gas at the same temperature , or vice-versa (from gas to liquid). • During melting and boiling, the potential energies of the particles are increased because the forces of attraction are being overcome; particles are breakin g out of their fixed positions (solid to l