DHS 12 First Law of Thermodynamics (Notes & Tutorial)

1 9749 Physics (2024) Topic 9: First Law of Thermodynamics Guiding Questions  How can temperature and heat be understood from both macroscopic and microscopic perspectives?  How does the energy transferred between a system and its environment relate to heat transfer and mechanical work done? 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. Introduction 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. Thermodynamics and its applications are relevant to our daily lives. Many researchers still actively investigate the behaviour of gases using computer simulation and other techniques. Environmental problems connected with Earth’s atmosphere, such as the de pletion of ozone layer, are motivations for such work. A better understanding of the behaviour of gases might lead to an improved characterisation and possible solutions to these problems. The application of thermodynamics pervades modern society e.g. car engines, air conditioners and power stations. However, an inevitable consequence of this energy conversion is the discharge of heat. This unwanted release of thermal energy into the environment is known as thermal pollution. One approach to reduce this is the development of alternative sources of energy, e.g. solar power. Another approach is to make things more efficient. Reducing the demand for energy should also be a personal and policy priority. 9749 H2 Physics Topic 9 First Law of Thermodynamics Year 5 (2024) DUNMAN HIGH SCHOOL

2 9749 Physics (2024) Topic 9: First Law of Thermodynamics (a) define and use the concepts of specific heat capacity and specific latent heat Specific heat capacity The specific heat capacity of a substance is defined as the heat per unit mass required to cause unit change in temperature. If the heat Q supplied to a mass m of the substance can cause its temperature to rise by T, then the specific heat capacity of the substance c is expressed mathematically as Qc m T  The unit of c is J kg−1 K−1. For example, if c of a substance is 100 J kg−1 K−1 then 100 J of thermal energy is required to increase the temperature of 1 kg of the substance by 1 K. Rearranging the above equation gives Q mc T  The heat capacity of an object C is heat required to cause a unit change in its temperature, i.e., QC T  , with a unit of J K−1. Rearranging give Q = CT. Comparing with the equation above, C = mc, i.e. the heat capacity of an object is the product of the specific heat capacity of the material and the mass of that object. Example 1 An air gun pellet, mass m and specific heat capacity c, hits a steel plate at speed v. During the impact, 50% of the pellet’s kinetic energy is converted to thermal energy in the pellet. What is the rise in temperature of the pellet? A 2 2 v c B 2 4 v c C 2 2 mv c D 2 4 mv c Ans: ( ) Heat transferred during the impact,   2 21 1 2 2 4 vQ mv mc T T c    

3 9749 Physics (2024) Topic 9: First Law of Thermodynamics Example 2 A piece of brass of mass of 1.0 kg undergoes three different processes involving change of energy: P: it is lifted vertically 2.0 m Q: it is heated from 15 oC to 20 oC R it is accelerated from rest to 10 m s−1 Given that the specific heat capacity of brass is 380 J K −1 kg−1, the processes, arranged in order of increasing energy change, are A PQR B QPR C QRP D PRQ Ans: ( ) Let the mass of brass = 1.0 kg, change of energy in P is      1.0 9.81 2.0 19.6 Jmg h   change of energy in Q is    1.0 380 20 15 1900 Jmc T    change of energy in R is   22 21 1 2 2 10 – 0 50 Jmv mu   Specific latent heat The specific latent heat of a substance is defined as the heat per unit mass required to change its phase without changing its temperature. For the change of phase between solid and liquid , it is known as the specific latent heat of fusion, and it occurs at the substance’s melting point. For the change of phase between liquid and gas, it is known as the specific latent heat of vaporisation, and it occurs at the substance’s boiling point. If the heat Q supplied to a substance can cause a change in phase of a mass m of the substance, then the specific latent heat of the substance L is expressed mathematically as QL m The unit of L is J kg−1. `Rearranging the above equation gives Q mL You may refer to Annex A and Annex B for the experimental determination of specific heat capacity and specific latent heat respectively.

4 9749 Physics (2024) Topic 9: First Law of Thermodynamics Example 3 A liquid is maintained at its boiling point by means of an electric heater. The constant rate at which liquid boils away is measured for two different powers of the heater as shown: power of heater rate of loss of mass of liquid P1 P2 m1 m2 For each power of the heater, P1 or P2, the rate of heat loss h to the environment is the same. Which expression is correct for the specific latent heat of vaporisation of the liquid? A 1 1 P m B 1 2 1 1 1 2 P P m m       C     1 2 1 2 P P m m   D     1 2 1 2 P P m m   Ans: ( ) 1 1 2 2 1 2 1 2 1 2 1 2 1 2 ----- (1) ----- (2) (1) (2) ( ) P m L h P m L h P P m L m L m m L P PL m m               Example 4 In a heating experiment, energy is supplied at a constant rate to a liquid in a beake r of negligible heat capacity. The temperature of the liquid rises at 4.0 K per minute just before it begins to boil. After 40 minutes all the liquid has boiled away. For this liquid, what is the ratio specific heat capacity specific latent heat of vaporisation ? A 1 10 K−1 B 1 40 K−1 C 1 160 K−1 D 1 640 K−1 Ans: ( )   v v v v 4 ----- (1)     0 2 (1 ----- ( ) 4 ) (2) 4 1 6 0 1 40 TP mc mct mL mLP t L L c c         

5 9749 Physics (2024) Topic 9: First Law of Thermodynamics (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 The internal energy of a substance 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. The thermodynamic state of a system is defined by specifying values of a set of measurable properties sufficient to determine all other properties. For fluid systems, typical properties are pressure, volume and temperature. The internal kinetic energy depends on the temperature and is the total energy of the atoms and molecules due to their translational, rotational and vibrational motion. The internal potential energy depends on the separation and is the total energy of the atoms and molecules due to in