A carbot freezer takes heat from water at `0^(@)C` inside it and rejects it to the room at a temperature of `27^(@)C`. The latent heat of ice is `336xx10^(3)Jkg^(-1)`. If 5kg of water at `0^(@)C` is converted into ice at `0^(@)C` by the freezer, then the energy consumed by the freezer is close to :

Options

A. `1.51 xx 10^(5)` J
B. `1.68 xx 10^(6)` J
C. `1.71 xx 10^(7)` J
D. `1.67 xx 10^(5)` J

Answer

D

Explanation

`DeltaH = mL = 5 xx 336 xx 10^(3) = Q_("sink")`
`Q_("sink")/Q_("source") =T_("sink")/(T_("source")) rArr Q_("source") =(T_("source"))/(T_("sink")) xx Q_("sink")`
Energy consumed by freezer
`therefore w_("output") = Q_("source") -Q_("soak") =Q_("sink") (T_("source")/T_("sink") -1)`
Given: `T_("source") = 27^(@) + 273 = 300 K`
`T_("sink") =0^(@) C + 273 = 273 K`
`W_("output") = 5 xx 336 xx 10^(3) ([300/273-1]) = 1.67 xx 10^(5)` J