Three blocks (A, B, and C) have initial temperatures of 700 K, 400K, and 100 K r

Question

Three blocks (A, B, and C) have initial temperatures of 700 K, 400K, and 100 K respectively and heat capacities C of 2 kJ/K, 1 kJ/K, and IkJ/K respectively. An auxiliary system can interact with these blocks in a reversible manner. In one complete cycle of reversible interactions, the auxiliary system is used to change the temperatures of the blocks. The net work transfer for the complete cycle is zero. a) What is the maximum temperature that can be obtained for one of the blocks b) c) Describe one possible cycle of reversible interactions using the system from b) using this auxiliary system? Give an example of a system that could be used to accomplish this task. that produces these temperature changes

Explanation / Answer

given three blovcks

Ta = 700 K

Ca = 2 kJ/K

Tb = 400 K

Cb = 1 kJ/K

Tc = 100 K

Cc = 1 kJ/K

A. as heat canot transfer from a body of higher temperature to a body of lower temperature

for an auxiliry unit of minute heat capacity

the maximum possible temperature is 700 K

B. one example of a system

let there be a gas of heat capacity c

then

it is initially at Ta = 700 K

then is brouht in touch with Tb

final temp = T1

c*(700 - T1) = 1000*(T1 - 400)

T1 = (1000*400 + 700c)/(1000 + c)

then it is brought into touch with c

final temp T2

c*(T1 - T2) = Cc(T2 - 100)

T2 = (cT1 + 100Cc)/(Cc + c)

T2 = (c(1000*400 + 700c)/(1000 + c) + 100*1000)/(1000 + c)

then is brought in touch wit A agaon final temp

c(T3 - T2) = Ca(700 - T3)

T3 = (700*2000 + c(c(1000*400 + 700c)/(1000 + c) + 100*1000)/(1000 + c))/(2000 + c)

now for c = 0

T3 = 700 K

hence a systyem with 0 heat cvapacity can work with maximum temperature oxf 700 K ( upper limit)

C. the cycle cshall be to bring the system in contact with A then B and then C and then repeat the process

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