A reversible heat engine, operation on Carnot cycle, between the temperature limits of 300 K and 1000 K produces 14 kW of power. If the calorific value of the fuel is 40,000 kJ/kg. The fuel consumption will be:

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  1. 1.4 kg/hr
  2. 1.8 kg/hr
  3. 2.0 kg/hr
  4. 2.2 kg/hr

Answer (Detailed Solution Below)

Option 2 : 1.8 kg/hr
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ST 1: UPSC ESE (IES) Civil - Building Materials
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Detailed Solution

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Concept:

For a reversible heat engine

where, Tmin is the minimum temperature and Tmax is the maximum temperature of the cycle.

Also,

where Q is the heat supplied to the engine and W is the work output of the engine

Q = ṁf × CV

Where, ṁf is the mass flow rate of fuel and CV is the calorific value of the fuel

Calculation:

Given, Tmin = 300 K, Tmax = 1000 K, W = 14 kW and CV of fuel = 40,000 kJ/kg

Q = ṁf × CV

f = 18 kg/hr

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