Question

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.

Answer 1

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

Explanation:

There are two heat transfers to be considered:

`"heat lost by ice cube" + "heat gained by liquid nitrogen" = 0`

`q_1 +q_2 =0`

`m_1cΔT + m_2L= 0`

`m_1 = "31 g"`

`c_1 = "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_2L = 0`

`m_2L = -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"`