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What is the loss of available energy associated with the transfer of 1000 kJ of heat from a constant temperature system at 600 K to another at 400 K when the environmental temperature is 300 K?
  • a)
    150 kJ
  • b)
    250 kJ
  • c)
    166·67 kJ
  • d)
    180kJ
Correct answer is option 'B'. Can you explain this answer?
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Loss of Available Energy Calculation:

Given:
- Heat transferred, Q = 1000 kJ
- Initial temperature, T1 = 600 K
- Final temperature, T2 = 400 K
- Environmental temperature, Tenv = 300 K

To calculate the loss of available energy, we can use the equation for the change in available energy, ΔA, which is given by:

ΔA = Q - Tenv * ΔS

Here, Q is the heat transferred, Tenv is the environmental temperature, and ΔS is the change in entropy.

1. Calculate the change in entropy:
ΔS = ΔS1 - ΔS2

2. Calculate the change in entropy for each system:
ΔS1 = Q / T1
ΔS2 = Q / T2

3. Calculate the total change in entropy:
ΔS = ΔS1 - ΔS2
= Q / T1 - Q / T2

4. Substitute the given values:
ΔS = (1000 kJ) / (600 K) - (1000 kJ) / (400 K)

5. Simplify the equation:
ΔS = (5/3) - (5/2)
= (10/6) - (15/6)
= -5/6

6. Calculate the loss of available energy:
ΔA = Q - Tenv * ΔS
= 1000 kJ - (300 K) * (-5/6)
= 1000 kJ + (250 kJ)
= 1250 kJ

Therefore, the loss of available energy associated with the transfer of 1000 kJ of heat from a constant temperature system at 600 K to another at 400 K when the environmental temperature is 300 K is 1250 kJ. However, none of the provided answer options match this value.
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