First Law of Thermodynamics
In the 18th and 19th century scientists observed several phenomena in which some quantities were getting transformed into another. Galvani reported that a charged metal could cause a dead frog's leg to twitch. Volta showed that this was a result of the passage of electric current. Volta developed a "voltaic cell" creating electricity from chemical reactions. Faraday, on the other hand, created chemical reactions using electricity. Oersted reported generating magnetic field from electricity and Seebeck generated electricity from heat laying foundations of thermoelectricity. Generation of electricity by changing magnetic field came as Faraday's law of electromagnetic induction in 1831. These interactions led the scientific community to think in terms of an indestructible form - called energy by Thomas Young in 1807- to change from one form to another. First law of thermodynamics is the law of conservation of energy, that is, the energy can be changed from one form to another but cannot be either created or destroyed.
Mechanically all energy can be considered as a sum of kinetic and potential energy of the constituent particles. Therefore, the first law could be thought of as the conservation of the sum of kinetic and potential energies of the constituent particles.
Heat and work are different forms of energy. A system can experience heat and work interactions at its boundary i.e. energy entering the system as heat can leave as work and vice versa. In a steam power plant for example work can be produced from steam only when heat is transfered to the steam. On the other hand, in metal working process, the work done on the system is partly used for deforming metal and the remainder is rejected as heat.
There is an equivalence of heat and work. Adding heat to a system can cause its temperature to increase. Similarly doing work on an insulated system (avoiding any heat exchange) can cause a similar effect. What is the relationship between heat and work? This question was answered by Joule. His experiments indicated that the number of units of work required to achieve a certain effect divided by the number of units of heat required to bring about the same effect is a constant. This constant is called the mechanical equivalent of heat, represented by symbol J and has a value of 4.1868E3 Nm/kcal when work is measured in Nm and heat in kcal. In SI units, J=1 Nm/J.
In the above experiments the final state of the system was different from the initial state. Joule also performed experiments involving cyclic processes such that heat and work undo each others effects. This means in such processes the initial and final states of the system are identical. In each cyclic process, when the sum of all work interactions, W, is equal to a constant times the sum of all heat interactions, Q. This constant is, again, the mechanical equivalent of heat, J. We can write,
∑W=J.∑Q
where summation is cyclic.
In words, first law of thermodynamics can be stated as follows:
Net work is proportional to net heat as a system executes a cyclic process.
where summation is cyclic.
In words, first law of thermodynamics can be stated as follows:
Net work is proportional to net heat as a system executes a cyclic process.
A system comprising 5kg of a mixture of air and nitrogen is initially at a pressure of 150 kN/m2 and a temperature of 300K. The mixture undergoes a process to a pressure of 300 kN/m2 and a temperature of 400K. During the process the heat transfer from the mixture is 10 kJ. 64 kJ of work is done on the mixture. What is the increase in the energy of the mixture?
Following the first process, the mixture undergoes a second process to a pressure of 150 kN/m2 and temperature of 300K. The mixture does 50 kJ of work. What is the magnitude and direction of heat transfer in the second process? Assume that pressure and temperature completely define the state of the mixture.
What is the change in energy of the mixture after it undergoes both processes sequentially?
A system is defined as any prescribed and identifiable collection of matter (Spalding, 1973). It is separated from its surroundings by a system boundary across which heat and work interactions take place. According to the first law of thermodynamics, for a system undergoing a change of state from 1 to 2,
E2-E1=Q-W
Where E is the energy of the system, Q is the heat added to the system and W is the work done by the system on its surroundings.
When the above system undergoes the process 1à 2, heat is taken away from the system and work is done on the system. Hence both Q and W are negative. Therefore, the change in energy of the system is
E2-E1=Q-W=-10-(-64)=54 kJ
Now if the system undergoes a process such that its pressure and temperature return to its initial values, the system has returned to its original state. Therefore, it has undergone a change in energy of -54 kJ. Hence, the heat transfer is -54+50 = -4 kJ.
4 kJ of heat has been taken away from the system.
Energy is a property. Hence, in a cyclic process there is no change in the value of energy. So when our system undergoes processes 1->2 and 2->3 sequentially, it experiences a zero change in energy.
References:
Spalding, D.B. & Cole, E.H., 1973, Engineering Thermodynamics 3ed, ELBS
