# A 31 g ice cube at its melting point is dropped into an insulated container of liquid nitrogen. How much nitrogen evaporates if it is at its boiling point of 77 K and has a latent heat of vaporization of 200 kJ/kg?

## Assume for simplicity that the specific heat of ice is a constant and is equal to its value near its melting point.

Jun 30, 2016

The ice cube will cause 62 g of nitrogen to evaporate.

#### Explanation:

There are two heat transfers to be considered:

$\text{heat lost by ice cube" + "heat gained by liquid nitrogen} = 0$

${q}_{1} + {q}_{2} = 0$

m_1cΔT + m_2L= 0

${m}_{1} = \text{31 g}$

${c}_{1} = \text{2.050 J·K"^"-1""g"^"-1}$

ΔT = T_f - T_i = "77 K - 273.15 K" = "-196.15 K"

q_1 = m_1cΔT = 31 color(red)(cancel(color(black)("g"))) × 2.050 "J"·color(red)(cancel(color(black)("K"^"-1""g"^"-1"))) × ("-196.15" color(red)(cancel(color(black)("K")))) = "-12 465 J"

${q}_{1} + {m}_{2} L = 0$

${m}_{2} L = - {q}_{1}$

m_2 = (-q_1)/L = ("+12 465" color(red)(cancel(color(black)("J"))))/(200 color(red)(cancel(color(black)("J")))·"g"^"-1") = "62 g"