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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
Copper: thermal conductivity = 390 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. A copper wire of diameter d = 10 millimeters runs from the reservoir to the camera. The camera is kept at temperature T(camera) = -100 Celsius.
Question 1: Heat flows from the camera at a rate Z = 2.9 Joules/sec. What is the length of the wire?
Answer: The cross-section area of the wire is
A = pi*r^2 = pi*(0.005 m)^2 = 7.85 x 10^(-5) m^2
The rate of heat transfer through the wire is
Q A*(delta T)
--- = k -----------
t L
Solve for length of wire, L:
t
L = --- * k*A*(delta T)
Q
1
= ---------- *(390 J/s*m*C)*(7.85 x 10^(-5) m^2)*(96 C)
2.9 J/s
= 1.0 m
Question 2: How much energy flows into the nitrogen reservoir every day?
Answer:
J s hour
2.9 --- * 3600 --- * 24 ---- = 2.5 x 10^5 J/day
s hour day
Question 3: What mass of liquid nitrogen boils off per day?
Answer: Heat required to boil m kilograms of liquid is
Q = m*(latent heat of vaporization) = m*Lv
Solve for mass m:
Q 2.5 x 10^5 J/day
m = --- = ------------------ = 1.25 kg/day
Lv 2.0 x 10^5 J/kg
This page maintained by Michael Richmond. Last modified Jan 13, 1998.
Copyright © Michael Richmond.
This work is licensed under a Creative Commons License.