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An ideal gas heat engine operates in Carnot cycle between 227°C and 127°C. It absorbs 6 x 10^4 cal of heat at higher temperature. Amount of heat converted to work is :

  1. A
    2.4 x 10^4 cal
  2. B
    3.6 x 10^4 cal
  3. C
    1.2 x 10^4 cal
  4. D
    6.4 x 10^4 cal

Solution & Step-by-step Explanation

The efficiency of a Carnot engine is given by the formula η = 1 - (T_c / T_h), where T_c is the temperature of the cold reservoir and T_h is the temperature of the hot reservoir. In this case, T_h = 227°C = 500 K and T_c = 127°C = 400 K. The efficiency is thus η = 1 - (400 / 500) = 1 - 0.8 = 0.2 or 20%. The amount of heat converted to work (W) can be found using the formula W = η Q_h, where Q_h is the heat absorbed at the higher temperature. Given Q_h = 6 x 10^4 cal, W = 0.2 6 x 10^4 cal = 1.2 x 10^4 cal.

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An ideal gas heat engine operates in Carnot cycle between 227°C and 127°C. It absorbs 6 x 10^4 cal of heat at higher temperature. Amount of heat converted to work is :
A
2.4 x 10^4 cal
B
3.6 x 10^4 cal
C
1.2 x 10^4 cal
D
6.4 x 10^4 cal

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