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1st Law of Thermodynamics

A carnot engi...

Question

A carnot engine extracts heat from water at $0^{0} C$ and rejects it to room at ${24.4}^{0} C$ . The work required by the refrigerator for every $1 k g$ of water converted into ice (latent heat of ice $= 336 k J / k g$ ) is:

30 k J

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336 k J

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11.2 k J

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24.4 k J

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Solution

The correct option is C $30 k J$
Temperature of sink $T_{L} = 0^{o} C = 273 K$
Temperature of source $T_{H} = {24.4}^{o} C = 297.4 K$
Efficiency of carnot refrigerator $β = \frac{T_{L}}{T_{H} - T_{L}} = \frac{273}{297.4 - 273} = 11.2$

Also to convert $1 k g$ of water into ice, $Q_{H} = 336$ $k J$
$∴$ Using $β = \frac{Q_{H}}{W}$

or , $11.2 = \frac{336 k J}{W}$
$⟹ W = 30 k J$

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