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Liquid nitrogen: boils at T(boil) = -196 Celsius latent heat of vaporization = 2.00 x 10^5 J/kg latent heat of fusion = 2.57 x 10^4 J/kg Aluminum: thermal conductivity = 240 J/s*m*C

One must keep an electronic camera must be very cold to avoid noisy images. A camera is connected to a reservoir of liquid nitrogen to chill it. The liquid nitrogen is at its boiling temperature. An aluminum wire of length L = 3 meters and diameter d = 6 millimeters runs from the reservoir to the camera.

**Question 1:**
Every hour, a mass of m = 43 g of nitrogen
evaporates. What is the rate of evaporation,
in kg/sec?

Answer: m = 43 g = 0.043 kg. 0.043 kg kg rate = ------------ = 1.2 x 10^(-5) --- 3600 sec sec

**Question 2:**
How much energy is required to flow into the liquid
nitrogen per second to maintain this evaporation?

Answer: Energy = (Latent heat of vaporization)*(mass) Energy mass ------ = (Latent heat of vaporization)* ---- sec sec = (2.00 x 10^5 J/kg) * 1.2 x 10^(-5) kg/s = 2.4 J/s

**Question 3:**
What is the temperature of the camera, at the other
end of the wire?

Answer: The rate of heat transfer from the vat of nitrogen to the camera is Q A * (delta T) --- = k * ------------- t L The cross-section area of the wire is A = pi*r^2 = pi*(0.003 m)^2 = 2.8 x 10^(-5) m^2 Solve for (delta T) Q L (delta T) = --- * ----- t k*A 3 m = (2.4 J/s) * ---------------------------------- (240 J/s*m*C)*(2.8 x 10^(-5) m^2) = 106 Celsius Now we can determine the temperature of the camera T(camera) = T(nitrogen) + (delta T) = -196 Celsius + 106 Celsius = -90 Celsius

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This page maintained by Michael Richmond.
Last modified Jan 13, 1997.
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Copyright © Michael Richmond. This work is licensed under a Creative Commons License.