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Transfer time of text

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2. The text of the Encyclopaedia Britannica is about 44 million words. For a sample of about 2000 words, the average word length was 5.1 characters per word.
a. Approximately how many characters are there in the encyclopedia? (Be sure to
allow for spaces and punctuation between words.)
b. How long would it take to transmit the text over a T-1 line at 1.544 Mbps? On a
fiber optic link at 2.488 Gbps?

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Let's assume that there is one space between words and a punctuation code every 6th word.

So 5/6 of the words will have the length of 6.1 characters (word+space) while 1/6 of the words are 7.1 characters in length (wore+punctuation+space).

This ...

Solution Summary

The solution explains in detail how to calculate the required values.

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Laplace heat transfer equations for thermocouple

See the following attachment and answer questions related to Laplace equation for temperature transfer, transient response, and graph plotting. All questions outline in attachments for better view of figure and equations. Text is mentioned below.

Questions 4

A thermocouple is a device commonly used to measure the temperature in, for example, boilers and engines. It has the advantage of directly giving out a voltage that is approximately proportional to the measured temperature. The thermo-voltage is, however, only a few millivolts.

In the block diagram of FIGURE 4, the output of the thermocouple, vT(t), is fed into an amplifier to give a sufficiently large signal to drive a signal processing stage. The signal processing stage includes an analogue-to-digital converter (ADC) to give an output to drive a digital display. A low-pass filter (LPF) is placed between the amplifier and the signal processing stage to remove noise that may be picked up from adjacent 'noisy' equipment and from 'mains' interference.

[FIG.4] (See Attachment! img001.jpg)

The thermocouple should ideally have a step change output to a step change in temperature. In practice this is not the case because the mass of the device introduces a thermal delay as it warms up or cools down to a new temperature. It can be shown that the temperature of the thermocouple is related to a step change in temperature by the equation:

[Eq.1] (See Attachment! img001.jpg)

The time constant depends upon the mass (in) and surface area (A) of the thermocouple, the thermal specific heat (c) of the material it is made from and also the heat transfer coefficient (h) between the thermocouple and its surroundings. Thus:

[Eq.] (See Attachment! img002.jpg)

4. (a) In FIGURE 5(a) the thermocouple is shown with an initial temperature the same as that for the ambient air, TA. It is then immersed into a tub of hot water at a constant temperature of Tw. Thus the applied step change in temperature is Del-T = Tw — TA. (See Attachment! img002.jpg)

(i) Write down the Laplace equation for equation (1).
(ii) Hence obtain the equation of the transient response of the thermocouple.
(iii) Plot the transient response using the data in TABLE B over a time period of about 4t.

[TABLE B] (See Attachment! img002.jpg)

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