Unformatted text preview: D L SE C T I O N 7B.S11 - Quiz 4D
Last 6 digits of student ID
______ _ Last name,
First three letters of your last name ___ N o boo k s o r not es. C a l c u l a t o r s O K . Show a l l you r w o r k b e l ow. A nsw e r s a l on e w i l l r e c e i v e no c r e d i t !
T h is q u i z h as t w o si d es! 1.
You are at the McMurdo research center in Antarctica studying some of the unique lifeforms
that live in unusually cold temperatures. The temperature outside at this time of the year is usually
around -20o C, but you hear that a storm is coming and the temperature will slowly drop to some lower
temperature. You need to finish the experiment and walk back to the main campus and want to make
old when you leave.
Your body produces energy as heat constantly (burning calories is how your body temperature
is stably higher than the room temperature) and the power produced is 0.03 W . You have specially
heavy clothes that are on average 5 c m thick (the average includes everything: boots, snow goggles,
scarf, gloves, etc.) and the effective total surface area of the clothes is 3 m2. The conductivity k of the
special material of your clothes is on average 7.5 10-6 W /(m K ).
You will have to walk for a while to reach the main campus. To remain safe, you need to
produce at least as much heat as you lose to the outside. Find the minimum temperature that you can
safely walk in so that your body will be stably at 36o C and you can avoid getting hypothermia. You want to know when the heat produced by your body equals the heat lost to the
atmosphere. Then you need to know what the heat ﬂow is.
This means that 0.03 W = I, where I is the heat ﬂow to the atmosphere.
j = -k Delta (T) / L = 7.5 x 10^(-6) W/(m K) x Delta(T) / 0.05 m
0.03 W = I = j A = Delta (T)_max x 4.5 x 10^(-4) W/K
D elta (T)_max = 0.03/0.00045 K = 66.7 K = 66.7 C (in Delta's, C and K are the same)
Delta (T)_max = 36 C - T_max = 66.7 C
T_max = 36 C - 66.7 C = -30.7 C Thermal flux:
Capacitor charging/discharging: 2. You have three circuits (label them 1, 2 and 3), each of the same type as the one shown
to the right. Each battery has an identical
. The values of the resistance and
capacitance in each circuit is unknown. The capacitor is initially completely uncharged. You
begin charging the capacitor in each circuit and you observe the current in each. The graph
below shows the current in each circuit as a function of time starting the instant the capacitor
begins to charge. a) Use the graph to rank the values of the resistance in each circuit from least to greatest. If any are equal
specify that as well. Briefly explain your reasoning. D elta (V)_r = - I R
at ﬁrst Delta (V) is the same for all the circuits (because, like speciﬁed in the text, they
h ave the same battery) then
where we used Delta (V)_r = - E.
It is clear from the graph that circuits 3 and 2 start from the same I, so they also have
the same R, while I_1 is smaller, meaning that R_1 is greater than R_2 = R_3
b) Use the graph to rank the time constants of each circuit from least to greatest (you can denote time constant
). If any are equal specify that as well. Briefly explain your reasoning. You can just read the graph for this.
You know that the time constant is proportional to how fast the exponential drops.
In this case, circuit 1 drops really fast (it becomes a half in 0.2 s), circuit 3 comes right
after (it becomes half after about 1.5 s) and circuit 2 has the largest time constant.
T_2 > T_3 > T_1 c) Use the results of parts a) and b) to rank the value of the capacitance in each circuit from least to greatest. If
any are equal specify that as well. Briefly explain your reasoning. T_i = R_i C_i
now, R_2 = R_3, but you know that T_2 > T_3, then C_2 > C_3
R_1 is the greatest, but T_1 is the smallest, then C_1 has to be the smallest in order to be
multiplied to R_1 and still be smaller than T_3 and T_2
C_2 > C_3 > C_1
Capacitor charging/discharging: ...
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- Spring '07
- Energy, Thermal Flux, Main Campus, unusually cold temperatures