b. the energy needed to melt 500 g of ice at 0°C.latent heat of ice is 340,000j/kg.
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I will assume you mean ice that is already at 0 °C and not ice that is colder than that, since ice that is colder than 0 °C will first have to be warmed up to 0 °C before it can melt, and you have no mentioned specific heat capacity, which would be required to calculate that.
A more precise figure for the latent head of *fusion* of water is 333.55 kJ/kg. Since you have 5 kg, you will need to pump 333.55 × 5 = 1667.75 kJ of heat into your ice to completely melt it.
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