Problem 1.36. In the course of pumping up a bicycle tire, a liter of air atatmospheric pressure is compressed adiabatically to a pressure of 7 atm. (Air ismostly diatomic nitrogen and oxygen.)(a) What is the final volume of this air after compression?(b) How much work is done in compressing the air?(c) If the temperature of the air is initially 300 K, what is the temperatureafter compression?Problem 1.45. As an illustration of why it matters which variables you hold fixecwhen taking partial derivatives, consider the following mathematical example. Lew = ry and æ = yz.(a) Write w purely in terms of x and z, and then purely in terms of y and z.(b) Compute the partial derivativesandand show that they are not equal. (Hint: To compute (dw/8x)y, use aformula for w in terms of z and y, not z. Similarly, compute (ðu/az);from a formula for w in terms of only z and z.)Problem 2.2. Suppose you flip 20 fair coins.(a) How many possible outcomes (microstates) are there?(b) What is the probability of getting the sequence HTHHTTTHTHHHTHH-HHTHT (in exactly that order)?(c) What is the probability of getting 12 heads and 8 tails (in any order)?Problem 2.3. Suppose you flip 50 fair coins.(a) How many possible outcomes (microstates) are there?(b) How many ways are there of getting exactly 25 heads and 25 tails?(c) What is the probability of getting exactly 25 heads and 25 tails?(d) What is the probability of getting exactly 30 heads and 20 tails?(e) What is the probability of getting exactly 40 heads and 10 tails?(f) What is the probability of getting 50 heads and no tails?(g) Plot a graph of the probability of getting n heads, as a function of n.Problem 2.6. Calculate the multiplicity of an Einstein solid with 30 oscillatorsand 30 units of(Doattempt to list all the microstates.)Problem 2.5. For an Einstein solid with each of the following values of N and q,list all of the possible microstates, count them, and verify formula 2.9.(a) N = 3, q = 4(b) N = 3, q = 5(c) N = 3, q = 6(d) N = 4, q = 2(e) N = 4, q = 3

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Problem 1.36. In the course of pumping up a bicycle tire, a liter of air at atmospheric pressure is compressed adiabatically to a pressure of 7 atm. (Air is mostly diatomic nitrogen and oxygen.) (a) What is the final volume of this air after compression? (b) How much work is done in compressing the air? (c) If the temperature of the air is initially 300 K, what is the temperature after compression?

Problem 1.36. In the course of pumping up a bicycle tire, a liter of air at atmospheric pressure is compressed adiabatically to a pressure of 7 atm. (Air is mostly diatomic nitrogen and oxygen.) (a) What is the final volume of this air after compression? (b) How much work is done in compressing the air? (c) If the temperature of the air is initially 300 K, what is the temperature after compression?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Concept explainers

Work and Heat Transfer

It is generally related to thermal engineering which tells about the use, creation, conversion and transfer of heat energy between the systems. It is also considered that to transfer heat from one source to another, transfer of masses is also required. There are various mechanisms by which, transfer of heat takes place i.e. thermal conduction, convection, radiation or by change of phase. All these mechanisms have their own specific features which sometimes occur simultaneously within the same system.

Question

Problem 1.36. In the course of pumping up a bicycle tire, a liter of air at
atmospheric pressure is compressed adiabatically to a pressure of 7 atm. (Air is
mostly diatomic nitrogen and oxygen.)
(a) What is the final volume of this air after compression?
(b) How much work is done in compressing the air?
(c) If the temperature of the air is initially 300 K, what is the temperature
after compression?
Problem 1.45. As an illustration of why it matters which variables you hold fixec
when taking partial derivatives, consider the following mathematical example. Le
w = ry and æ = yz.
(a) Write w purely in terms of x and z, and then purely in terms of y and z.
(b) Compute the partial derivatives
and
and show that they are not equal. (Hint: To compute (dw/8x)y, use a
formula for w in terms of z and y, not z. Similarly, compute (ðu/az);
from a formula for w in terms of only z and z.)
Problem 2.2. Suppose you flip 20 fair coins.
(a) How many possible outcomes (microstates) are there?
(b) What is the probability of getting the sequence HTHHTTTHTHHHTHH-
HHTHT (in exactly that order)?
(c) What is the probability of getting 12 heads and 8 tails (in any order)?
Problem 2.3. Suppose you flip 50 fair coins.
(a) How many possible outcomes (microstates) are there?
(b) How many ways are there of getting exactly 25 heads and 25 tails?
(c) What is the probability of getting exactly 25 heads and 25 tails?
(d) What is the probability of getting exactly 30 heads and 20 tails?
(e) What is the probability of getting exactly 40 heads and 10 tails?
(f) What is the probability of getting 50 heads and no tails?
(g) Plot a graph of the probability of getting n heads, as a function of n.
Problem 2.6. Calculate the multiplicity of an Einstein solid with 30 oscillators
and 30 units of
(Do
attempt to list all the microstates.)
Problem 2.5. For an Einstein solid with each of the following values of N and q,
list all of the possible microstates, count them, and verify formula 2.9.
(a) N = 3, q = 4
(b) N = 3, q = 5
(c) N = 3, q = 6
(d) N = 4, q = 2
(e) N = 4, q = 3

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letter d