A large fridge freezer is to extract 80 kJ of energy every second from inside of the fridge, maintained at temperature of -3 0C, and to dump it to the air outside which is at 30 0C. To do so, the fridge consumes 7 kW of electrical energy which is also converted and dissipated as heat to the surrounding air Calculate the entropy change per second in the surrounding air and that inside the fridge. Show that such a fridge freezer can never be realised in practice. What is the minimal electrical power necessary to achieve the operation of this fridge? If the electrical power used is to remain at 7kJ/s, but we still require to extract 80 kW of heat from inside, what is the lowest temperature in the fridge that we could theoretically hope to achieve? The fridge could be made to operate in the reverse mode, extracting 80 kJ of heat every second from a hot environment (say steam at 100 0C ), converting some of this energy to useful work (e.g. electrical energy) and then dumping the rest as heat to the surrounding air at 30 0C.
A large fridge freezer is to extract 80 kJ of energy every second from inside of the fridge, maintained at temperature of -3 0C, and to dump it to the air outside which is at 30 0C. To do so, the fridge consumes 7 kW of electrical energy which is also converted and dissipated as heat to the surrounding air
- Calculate the entropy change per second in the surrounding air and that inside the fridge.
- Show that such a fridge freezer can never be realised in practice.
- What is the minimal electrical power necessary to achieve the operation of this fridge?
- If the electrical power used is to remain at 7kJ/s, but we still require to extract 80 kW of heat from inside, what is the lowest temperature in the fridge that we could theoretically hope to achieve?
The fridge could be made to operate in the reverse mode, extracting 80 kJ of heat every second from a hot environment (say steam at 100 0C ), converting some of this energy to useful work (e.g. electrical energy) and then dumping the rest as heat to the surrounding air at 30 0C.
- What is the minimum amount of heat per second that has to be dumped to the air?
- Using your answer to part (e), show that the maximum useful work that we can hope to obtain from this operation is around 15 kW (i.e. show that the efficiency of this machine is only 15/80 = 18.7 %).
- Why can’t the efficiency of this machine ever be 100 % (i.e. why can’t we hope to design an engine that converts all of the extracted 80 kJ/s of heat completely to work)?
2) In an experiment, a 0.001 (mole fraction) solution of polysaccharide in water is made and is placed in the compartment A (see Figure below). Compartment B is filled with pure water. The two compartments are separated by a porous semi-permeable membrane that allows the exchange of water molecules between the two compartments, but not that of the larger polysaccharide molecules
- a) Show that the chemical potential of water in compartment A is lower than that in compartment B by 2.48 J/mol.
- b) As a result of this chemical potential difference, water molecules will move from compartment B to compartment A. This causes the pressure in compartment A, relative to that in B, to increase. How would this affect the chemical potential of water in compartment B? When would the diffusion of water from B to A cease (i.e. equilibrium is achieved)?
- c) Using your answer to part (b), work out the difference between the pressure in compartment A and B when equilibrium is achieved.
You may assume that the chemical potential of molecules in a liquid at pressure P2 relative to that, for the same liquid, at pressure P1 is given by the formula: Vm (P2 - P1), where Vm is the molar volume of the liquid. For water take Vm =18 cm3/mol and assume the temperature of the apparatus is 298 K.
- e) What is this pressure difference normally called?
3) Ammonia has a pKb=4.75. Work out how much ammonia is in the form of NH4+ in a 0.01 Molar solution at various pH values, ranging from 1 to 12 in steps of 1 pH unit? Plot a graph of amount of the NH4+ in the solution as a function of pH and comment on the shape of the graph.
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