Question

How many grams of water at 55 °C is needed to melt 2000 g of ice at 0 °C?

Answer 1

Answer:

2903 g

Explanation:

Given:

$m_i = 2000~g$

$t_i = 55^oC$

$t_f = 0^oC$

The final equilibrium temperature of this system should be 0 degrees Celsius, as we only melt the ice, so all of the heat lost by the water at 55 degrees Celsius will be used to melt ice. Heat given off by the water is described by:

$Q_1 = c_w m_w (t_i - t_f)$

Heat gained by the ice:

$Q_2 = \Delta H_{fus} m_i$

Heat gained should be equal to the heat lost:

$c_w m_w (t_i - t_f) = \Delta H_{fus} m_i$

Solve for the mass of water:

$m_w = \frac{\Delta H_{fus} m_i}{c_w (t_i - t_f)} = \frac{334~J/g\cdot 2000~g}{4.184~J/g^oC\cdot (55^oC - 0^oC)} = 2903~g$