Some ceramic materials will become superconducting if immersed in liquid nitroge

Question

Some ceramic materials will become superconducting if immersed in liquid nitrogen. In an experiment, a 0.220 kg piece of such material at 20°C is placed in liquid nitrogen at its boiling point to cool in a perfectly insulated flask, which allows the gaseous N2 immediately to escape. How many liters of liquid nitrogen will be boiled away in doing this operation? (Take the specific heat of the ceramic material to be the same as that of glass, and take the density of liquid nitrogen to be 0.80 103 kg/m3.)

Explanation / Answer

mass of glass: m = 0.220 kg

specific heat of glass: C = 0.84 kJ/kg-°K

glass temperature: T = 20°C

mass of nitrogen: m' = V,

boiling point of nitrogen: T' = -195.7 °C

density of nitrogen: = 0.8 x 10^3 kg/m^3

latent heat of vaporization of nitrogen: 201 kJ/kg

Q = mCT = 0.22*0.84*[20 -(-195.7)] = 39.86 kJ

This amount of heat is available to vaporize the nitrogen: Q = m'L = VL = 0.8 x 10^3 c x V x 201

39.86 =  0.8 x 10^3 x V x 201

V = 39.86 /  0.8 x 10^3 x 201

V = 0.00024789 m^3

V = 0.24789 L

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