First Law of a Closed System Undergoing a Cycle
First Law of a Closed System Undergoing a Cycle :
The first law of thermodynamics states that during any cycle a system undergoes the cyclic integral of heat is equal to the cyclic integral of the work.
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| Fig.1 First Law of Thermodynamics |
To illustrates this, consider the gas as a system in the container as shown in Fig.1. Let this system go through a cycle that is comprised of two processes. In the first process (1 – 2) the work is done on the system and the temperature of system increased from t₁ to t₂. Let the system then returned to its initial state i.e., to a temperature t₁ by transferring heat from the system until the cycle has been completed. This process is represented by path 2 – 1. When the amount of the work and heat were compared, it was found these two quantities (expressed in consistent units) are equal. This forms the basis of first law of thermodynamics which can be expressed in the form of equation.
∮ dQ = ∮ dW ……..(i)
where ∮ dQ = cyclic integral of heat transfer which represents the net heat transfer during the cycle.
∮ dW = cyclic integral of work transfer which represent net work transfer during the cycle. Consider a cycle as shown in Fig.2. The first of thermodynamics can be expressed as
Q₁₂ + Q₂₃ + Q₃₁ = W₁₂ + W₂₃ + W₃₁ …..(ii)
where the symbol Q and W with their subscripts represent the amount of heat transfer and work transfer for each of the processes making up the cycle. Thus, from equations (I) and (ii).
∮ dQ = Q₁₂ + Q₂₃ + Q₃₁
∮ dW = W₁₂ + W₂₃ + W₃₁
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| Fig . 2 |
∈ R, a ≤ x < b are known as semi-open or semi-closed intervals . (a,…
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