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Question
Let Ta and Tb be the final temperatures of the samples A and B, respectively, in the previous question.
(a) Ta < Tb
(b) Ta = Tb
(c) Ta > Tb
(d) The relation between Ta and Tb cannot be deduced.
(a) Ta < Tb
(b) Ta = Tb
(c) Ta > Tb
(d) The relation between Ta and Tb cannot be deduced.
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Solution
(a) Ta < Tb
As sample B is undergoing expansion through an isothermal process, its initial and final temperatures will be same, i.e. Tb. On the other hand, sample A is at the same initial state as B, such that the initial temperature of A is ​Tb and it is expanding through an adiabatic process in which no heat is supplied. Therefore, sample A will expand at the cost of its internal energy and its final temperature will be less than its initial temperature.
This implies that Ta < Tb.
As sample B is undergoing expansion through an isothermal process, its initial and final temperatures will be same, i.e. Tb. On the other hand, sample A is at the same initial state as B, such that the initial temperature of A is ​Tb and it is expanding through an adiabatic process in which no heat is supplied. Therefore, sample A will expand at the cost of its internal energy and its final temperature will be less than its initial temperature.
This implies that Ta < Tb.
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