Question

Consider two 35-gram ice cubes, each initially at -5°C. One is dropped into a at container filled with 0.1 kg of liquid nitrogen (initially the boiling point of nitrogen); the other cube is dropped into a container filled with 1 kg of (liquid) water, initially at 5°C. Assume that no heat is lost through either container (or into the atmosphere)

a) Describe what happens to each ice cube (and why)

b) If (Lv)Nitrogen =48 kcal/kg, (LF)Nitrogen = 6.1 kcal/kg, and cNitrogen =0.15 kcal/(kg °C), determine how much heat would be needed to produce 100 grams of nitrogen gas at 20°C.

c).Determine the final (equilibrium) temperature of the icewater mixture.

d) Determine the phase (ie., liquid or solid) corresponding to the equilibrium temperature you obtained in part (c).

Answer 1

Given mass of ice cubes each m = 35 g = 0.035 kg, temperature of ice is Ti - 5 0C
   liquid nitrogen mass M = 0.1 kg, boiling point is Tb - 195.8 0C

we know that the boiling point of nitrogen is less than -5 0C so the ice cube will loss heat energy and nitrogen (liquid) gains heat energy

ice cube dropped in water container at 5 0C , ice cube melts become liq , and water will loss heat energy , ice cube gain heat energy

b)

   mass of nitrogen gas is 100 g

   q = 0.1*4184+ 0.1*627.6(20+195.8) J
  
   q = 13962.008 J

c) ice water mixure

   mLf + m C (T+5) = Mw*Cw(T-5)

   0.035*334+0.035*2108(T-5) = 1*4180(T-5)
   T = 5.002 0C

d) the phase is liquid