# Physics 212, Quiz #4a: Jan 9, 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

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

```