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An air refrigerator of 10 ton capacity operates in Bell Coleman cycle between pressure limits of 1 bar and 4 bar. Air at inlet of compressor is at 1 bar and 253 K. Air at exit of cooler is at 313 K. After air is cooled to 290 K at constant pressure in cooler, it is allowed to expand isentropically to 1 bar in expansion cylinder where temperature limit of cycle. Cold air is then sent to cold chamber to extract heat (Refrigerating effect) determine COP of refrigerator.
  • a)
    1.5
  • b)
    2.05
  • c)
    3.1
  • d)
    3.6
Correct answer is option 'B'. Can you explain this answer?
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An air refrigerator of 10 ton capacity operates in Bell Coleman cycle ...

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An air refrigerator of 10 ton capacity operates in Bell Coleman cycle ...
Given Data:
- Capacity of the air refrigerator (Qin) = 10 tons
- Pressure limits: P1 = 1 bar, P2 = 4 bar
- Inlet conditions of the compressor: P1 = 1 bar, T1 = 253 K
- Exit conditions of the cooler: T3 = 313 K
- Temperature after cooling in the cooler: T4 = 290 K
- Pressure after expansion in the expansion cylinder: P4 = 1 bar
- Temperature limit of the cycle: T2

To find: Coefficient of Performance (COP) of the refrigerator

The Bell Coleman refrigeration cycle consists of the following processes:
1. Compression
2. Cooling at constant pressure
3. Expansion
4. Heating at constant pressure

Let's calculate the values required for finding the COP:

1. Compression Process:
- Given: P1 = 1 bar, T1 = 253 K
- Assumption: Isentropic compression (s1 = s2)
- The specific entropy at state 1 (s1) can be determined using air tables or software. Let's assume s1 = x kJ/kg.K
- The specific enthalpy at state 1 (h1) can be determined using air tables or software.

2. Cooling Process:
- Given: T3 = 313 K
- The specific enthalpy at state 3 (h3) can be determined using air tables or software.

3. Expansion Process:
- Given: P4 = 1 bar
- Assumption: Isentropic expansion (s3 = s4)
- The specific entropy at state 3 (s3) can be determined using air tables or software.
- The specific enthalpy at state 3 (h3) can be determined using air tables or software.

4. Heating Process:
- Given: T4 = 290 K
- The specific enthalpy at state 4 (h4) can be determined using air tables or software.

Now, we can calculate the COP using the following formula:
COP = Refrigerating effect / Work input = (h1 - h4) / (h2 - h1)

Refrigerating effect (Qin) can be determined using the formula:
Qin = m_dot * (h3 - h4)

Work input (W) can be determined using the formula:
W = m_dot * (h2 - h1)

Finally, by substituting the values, we can calculate the COP of the refrigerator.
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An air refrigerator of 10 ton capacity operates in Bell Coleman cycle between pressure limits of 1 bar and 4 bar. Air at inlet of compressor is at 1 bar and 253 K. Air at exit of cooler is at 313 K. After air is cooled to 290 K at constant pressure in cooler, it is allowed to expand isentropically to 1 bar in expansion cylinder where temperature limit of cycle. Cold air is then sent to cold chamber to extract heat (Refrigerating effect) determine COP of refrigerator.a)1.5b)2.05c) 3.1d)3.6Correct answer is option 'B'. Can you explain this answer?
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