# Physics 212, Quiz #4b: Jan 8, 1998

Show all work -- you may receive partial credit!

```   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

```