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Nitrogen is extremely cold in its liquid phase.  It is used in the cryopreservation of small tissue samples and in cryosurgery to freeze and destroy diseased tissues.  Liquid nitrogen can be produced from nitrogen gas using the Hampson-Linde cycle (Figure 1).Figure 1  Hampson-Linde cycle apparatus used to liquefy nitrogenThe cycle begins by compressing nitrogen gas and forcing it through a coil in an external cooler that contains dry ice.  The gas proceeds to a heat exchanger, where it cools further due to the countercurrent heat exchange with colder nitrogen gas returning from a later stage of the cycle; this process is known as regenerative cooling.  The gas is subsequently forced through a narrow valve, where it expands and cools significantly upon exiting.  As a result, a portion of the gas becomes liquefied.The temperature change of the gas exiting the valve is described by the Joule-Thomson effect, which occurs without heat transfer with the surroundings.  Finally, the liquefied nitrogen is collected, and the remaining gas is sent through the regenerative cooler back to the compressor to reenter the cycle.  The physical properties of nitrogen are given in Table 1.Table 1  Thermal Properties of NitrogenBoiling point at STP 77 KMelting point at STP 63 KSpecific heat (liquid phase) 2 kJ/kg⋅KHeat of vaporization 400 kJ/kgHeat of fusion 50 kJ/kg Question 41Which thermodynamic quantity involved in the Hampson-Linde cycle is a state function?A.Entropy of nitrogen, because it describes an equilibrium state of the systemB.Entropy of nitrogen, because it describes a path to an equilibrium state of the systemC.Work done by the compressor, because it describes an equilibrium state of the systemD.Work done by the compressor, because it describes a path to an equilibrium state of the system

Question

Nitrogen is extremely cold in its liquid phase.  It is used in the cryopreservation of small tissue samples and in cryosurgery to freeze and destroy diseased tissues.  Liquid nitrogen can be produced from nitrogen gas using the Hampson-Linde cycle (Figure 1).Figure 1  Hampson-Linde cycle apparatus used to liquefy nitrogenThe cycle begins by compressing nitrogen gas and forcing it through a coil in an external cooler that contains dry ice.  The gas proceeds to a heat exchanger, where it cools further due to the countercurrent heat exchange with colder nitrogen gas returning from a later stage of the cycle; this process is known as regenerative cooling.  The gas is subsequently forced through a narrow valve, where it expands and cools significantly upon exiting.  As a result, a portion of the gas becomes liquefied.The temperature change of the gas exiting the valve is described by the Joule-Thomson effect, which occurs without heat transfer with the surroundings.  Finally, the liquefied nitrogen is collected, and the remaining gas is sent through the regenerative cooler back to the compressor to reenter the cycle.  The physical properties of nitrogen are given in Table 1.Table 1  Thermal Properties of NitrogenBoiling point at STP 77 KMelting point at STP 63 KSpecific heat (liquid phase) 2 kJ/kg⋅KHeat of vaporization 400 kJ/kgHeat of fusion 50 kJ/kg Question 41Which thermodynamic quantity involved in the Hampson-Linde cycle is a state function?A.Entropy of nitrogen, because it describes an equilibrium state of the systemB.Entropy of nitrogen, because it describes a path to an equilibrium state of the systemC.Work done by the compressor, because it describes an equilibrium state of the systemD.Work done by the compressor, because it describes a path to an equilibrium state of the system

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Solution

The correct answer is A. Entropy of nitrogen, because it describes an equilibrium state of the system.

A state function is a property of a system that depends only on the current state of the system, not on the way in which the system acquired that state. Entropy is a state function because it is a measure of the disorder or randomness of a system and only depends on the current state of the system.

On the other hand, work done by the compressor is not a state function because it depends on the path taken to reach the current state. The work done by the compressor can vary depending on the process (path) taken to compress the gas. Therefore, options C and D are incorrect.

Option B is also incorrect because while entropy does indeed describe a path to an equilibrium state of the system, this does not make it a state function. The key characteristic of a state function is that it depends only on the current state of the system, not the path taken to get there.

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