A Carnot refrigerator extracts heat from water at 0 -C and rejects it to a room at 24-4 -C- The work required by the refrigerator for every 1 kg of water converted into ice isLatent heat of ice - 336 kj kg -1

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Standard XII

Physics

Carnot Cycle

A Carnot refr...

Question

A Carnot refrigerator extracts heat from water at 0 $^{\circ}$ C and rejects it to a room at 24.4 $^{\circ}$ C. The work required by the refrigerator for every 1 kg of water converted into ice is
(Latent heat of ice = 336 kj kg $^{- 1}$ )

24.4 k j

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30 k j

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336 k j

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11.2 k j

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Solution

The correct option is B $30 k j$
Given,
$L = 336 K J / k g$
$m = 1 k g$
$T_{1} = 0^{0} C = 273 K$
$T_{2} = {24.4}^{0} C = 24.4 + 273 = 297.4 K$

Heat, $Q = m L$
$Q = 1 \times 336 k = 336 k J$

Coeffiient of performance( $β$ ) $= \frac{T_{1}}{T_{2} - T_{1}} = \frac{Q}{W}$

$\frac{273}{297.4 - 273} = \frac{336 \times 1000}{W}$

$W = 30 k J$
The work done is $30 k J$ .
The correct option is B.

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A Carnot refrigerator extracts heat from water at 0∘C and rejects it to a room at 24.4∘C. The work required by the refrigerator for every 1 kg of water converted into ice is(Latent heat of ice = 336 kj kg−1)

The correct option is B 30kjGiven,L=336KJ/kgm=1kgT1=00C=273KT2=24.40C=24.4+273=297.4KHeat, Q=mLQ=1×336k=336kJCoeffiient of performance(β)=T1T2−T1=QW273297.4−273=336×1000WW=30kJThe work done is 30kJ. The correct option is B.

A Carnot refrigerator extracts heat from water at 0 $^{\circ}$ C and rejects it to a room at 24.4 $^{\circ}$ C. The work required by the refrigerator for every 1 kg of water converted into ice is
(Latent heat of ice = 336 kj kg $^{- 1}$ )