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Chapter 10: Problem 63

Mark the correct options (A) A system \(X\) is in thermal equilibrium with \(Y\) but not with \(Z\). The system \(Y\) and \(Z\) may be in thermal equilibrium with each other. (B) A system \(X\) is in thermal equilibrium with \(Y\) but not with \(Z\). The system \(Y\) and \(Z\) are not in thermal equilibrium with each other. (C) A system \(X\) is neither in thermal equilibrium with \(Y\) nor with \(Z\). The systems \(Y\) and \(Z\) must be in thermal equilibrium with each other. (D) A system \(X\) is neither in thermal equilibrium with \(Y\) nor with \(Z\). The systems \(Y\) and \(Z\) may be in thermal equilibrium with each other.

Short Answer

Expert verified
The correct options are (A), (B), and (D), as they all present possible scenarios based on the concept of thermal equilibrium. In each case, nothing contradictory to the definition of thermal equilibrium is presented, while option (C) cannot be concluded based on the given information.

Step by step solution

01

Option (A)

System \(X\) is in thermal equilibrium with \(Y\) but not with \(Z\). This means \(X\) and \(Y\) are at the same temperature, but \(X\) and \(Z\) are not. However, nothing can be concluded about the thermal equilibrium between system \(Y\) and \(Z\) from the given information. So, option (A) is possible and marked as correct.
02

Option (B)

System \(X\) is in thermal equilibrium with \(Y\) but not with \(Z\). This means \(X\) and \(Y\) are at the same temperature, but \(X\) and \(Z\) are not. Furthermore, it is given that \(Y\) and \(Z\) are not in thermal equilibrium, which is possible as we do not have any information contradictory to this. So, option (B) is also possible, and it is marked as correct.
03

Option (C)

System \(X\) is neither in thermal equilibrium with \(Y\) nor with \(Z\). This means that \(X\) is at a different temperature than both \(Y\) and \(Z\). However, it cannot be concluded that systems \(Y\) and \(Z\) must be in thermal equilibrium with each other based solely on this information. So, option (C) is not correct.
04

Option (D)

System \(X\) is neither in thermal equilibrium with \(Y\) nor with \(Z\). This means that \(X\) is at a different temperature than both \(Y\) and \(Z\). It is given that systems \(Y\) and \(Z\) may be in thermal equilibrium with each other, which implies that both possibilities are considered: \(Y\) and \(Z\) being in thermal equilibrium and not being in thermal equilibrium. So, option (D) is possible and marked as correct. In conclusion, options A, B, and D are the correct options based on the concept of thermal equilibrium.

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