Tutorials in Introductory Physics
1st Edition
ISBN: 9780130970695
Author: Peter S. Shaffer, Lillian C. McDermott
Publisher: Addison Wesley
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Chapter 13.2, Problem 2aT
To determine
The nature of work done on the gas by the piston.
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A gas undergoes the cyclic process shown in the PV
diagram at right. In the process abc, the system
absorbs 4500 J of heat. The internal energy of the
gas at a is U₁= 600 J.
(b)
(c)
How much work is done on or by the gas
from a to b?
How much work is done on or by the gas
when it goes from b to c ? Note that the vertical scale
is measured in kilo-Pa-100 kPa -105 Pa
[1 Liter = 10³ m³]
100
The net heat absorbed by the gas during the complete cycle is 1000 J.
(d) Determine the heat entering or leaving in the process c to a
50
a
20
Use the First Law of Thermodynamics to determine the internal energy of the gas at c, Uc
60
C
Liters
In the pV diagram shown in the figure (Figure 1), 80.0 J of work was done by 0.0610 mole of ideal gas during an adiabatic process.
a) How much heat entered or left this gas from a to b? Express your answer in joules.
b) By how many joules did the internal energy of the gas change? Express your answer in joules.
c) What is the temperature of the gas at b? Express your answer in kelvins.
The porous catalyst pellet shown in Figure 1 has an overall radius R and a
thermal conductivity k (which may be assumed constant). Because of the chemical
reaction occurring within the porous pellet, heat is generated at a constant rate
of Se cal/em s. Heat is lost at the outer surface of the pellet to a gas stream at a
constant temperature T, by convective heat transfer coefficient h.
Gas
bemperature T,
Figure I. Sphere with internal heat
generation
Answer the following questions
(a) Make a list of assumptions that apply to the above situation.
(b) Set up the differential equation by making a shell energy balance. Show the
units for all variables that are used.
(c) Specify the proper boundary conditions.
(d) Integrate the differential equation with the above boundary conditions to
obtain an expression for the temperature profile, and make a sketch of the
function profile T(r)
(e) What is the limiting form of T(r) when h co?
(f) What is the maximum temperature in the system?
(g)…
Chapter 13 Solutions
Tutorials in Introductory Physics
Ch. 13.1 - Prob. 1aTCh. 13.1 - In the space provided, draw an arrow to indicate...Ch. 13.1 - Prob. 1cTCh. 13.1 - Prob. 1dTCh. 13.1 - Prob. 1eTCh. 13.1 - Prob. 2aTCh. 13.1 - Prob. 2bTCh. 13.1 - Consider the following student dialogue. Student...Ch. 13.1 - Sketch the process described in section II on the...Ch. 13.1 - Prob. 3bT
Ch. 13.1 - Prob. 4aTCh. 13.1 - A student looks up the molar masses and finds the...Ch. 13.1 - Prob. 4cTCh. 13.2 - Recall the definition of work done on an object by...Ch. 13.2 - Prob. 1bTCh. 13.2 - Prob. 1cTCh. 13.2 - Prob. 2aTCh. 13.2 - Does the internal energy of a gas in an insulated...Ch. 13.2 - Two students are discussing process 1: Student 1:...Ch. 13.2 - Imagine that the cylinder from section II is no...Ch. 13.2 - In process 2, is the heat transfer to the gas...Ch. 13.2 - Prob. 3cTCh. 13.2 - Prob. 4aTCh. 13.2 - In process 1 (section II) you did not need to...Ch. 13.2 - In process 2 (section III) you did not need to...Ch. 13.2 - Prob. 4dTCh. 13.2 - How does the compression in process 3 differ from...Ch. 13.2 - A student is considering process 3: “The...
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- A volume of air (assumed to be an ideal gas) is first cooled without changing its volume and then expanded without changing its pressure, as shown by the path abc in the figure (Figure 1). Take the graduation po = 3.0 x 10°Pa and the graduation V = 0.06. Correct Part B How much heat does the air exchange with its surroundings during the process abc? Express your answer in joules using two significant figures. Figure Hνα ΑΣφ Р (Рa) Qabe = 4000 J a Submit Previous Answers Request Answer PoF b' X Incorrect; Try Again; One attempt remaining V (m³) Vo Part Carrow_forwardPart B A container holds a sample of ideal gas in thermal equilibrium, as shown in the figure. (Figure 1) One end of the container is sealed with a piston whose head is perfectly free to move, unless it is locked in place. The walls of the container readily allow the transfer of energy via heat, unless the piston is insulated from its surroundings. Starting from equilibrium at point 0, what point on the pV diagram will describe the ideal gas after the following process? "Immerse the container into a large water bath at the same temperature, and very slowly push the piston head further into the container." • View Available Hint(s) O point 1 O point 2 O point 3 O point 4 O point 5 O point 6 O point 7 O point 8 Submit Previous Answers X Incorrect; Try Again; 4 attempts remaining The volume of the gas cannot remain constant because the piston head has moved further into the container. Part C Starting from equilibrium at point 0, what point on the pV diagram will describe the ideal gas…arrow_forwardThe graph in Figure 1.1 shows one mole of monoatomic gas at initial temperature of 40 ˚C and volume 2 L expanding isobarically at a constant pressure of 2.5 × 105 Pa to 5 L. It is then cooled down at constant volume to a pressure of 1.2 × 105 Pa. The gas is finally compressed isothermally back to its initial state. Calculate i. the work done in process AB. ii. the amount of heat absorbed from A to B iii. the work done by the gas from C to A. iv. the total work done in the complete process.arrow_forward
- The figure to the right shows a pV-diagram for 0.0040 mole of ideal H2 gas. The temperature of the gas does not change during the segment bc. What volume does this gas occupy at point c?arrow_forwardA gas undergoes the process shown in the diagram below. During the process AB, the internal energy of the gas decreases and a certain amount of heat Q goes out of the system for the process CA. Use this information to answer the questions below. Options for each selection is Positive, Negative, or Zero (check attached image) (a) What are the signs of W (work done by the gas), Q, and ΔU for the process CA?(b) What are the signs of W (work done by the gas), Q, and ΔU for the process AB?(c) What are the signs of W (work done by the gas), Q, and ΔU for the process BC?arrow_forwardThe pV diagram in the figure (Figure 1) shows a process abc involving 0.350 mol of an ideal gas. What was the temperature of this gas at points a, b, and c? How much heat had to be put in during the process to increase the internal energy of the gas by 1.30×104 J ?arrow_forward
- The temperature at state A is 20.0°C, that is 293 K. During the last test, you have found the temperature at state D is 73.0 K and n = 164 moles for this monatomic ideal gas. What is the change in thermal energy for process A to D, in MJ (MegaJoules)? Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement. P (atm) 4 3 ID B +V (m) 4 5arrow_forwardProblem 4: An ideal diatomic gas in a cylinder near room temperature undergoes the cyclic process shown. The four steps in the process are labeled A, B, C, and D. 1 (b) P2 V2 Volume Vị For each of the steps, A, B, C, D, determine whether each of the following is positive, negative, or zero: The work done on the gas. The change in energy content of the gas. The heat added to the gas. Express answers in terms of P1, P2, V1, and V2, then determine the sign. a) Make the table below showing, for each of the four steps, the sign (+, -, or 0) of W, Q and AU. AU B D b) Compute the net heat added, the net work done, and the net change in internal energy for one complete cycle.arrow_forwardConsider a thermal engine filled with N molecules of a monatomic ideal gas. The gas undergoes a cyclic transformation, as shown. (Figure 1) Processes AB and CD are isothermal (constant temperature), and processes BC and DA are isochoric (constant volume). The quantities p1, p2, V1, and V2 are defined in the figure. For example, when the gas is in state A, it has pressure p2 and volume V1; when the gas is in state B, it has volume V2, but the pressure is not given. 1. What is the change in internal energy UB−UA during the process AB? What is the change in internal energy UD−UC during the process CD? Express the change in internal energies in terms of p1, p2, V1, and/or V2. Separate your answers with a comma. 2. What is the change in internal energy UC−UB during the process BC? What is the change in internal energy UA−UD during the process DA? Express the change in internal energies in terms of p1, p2, V1, and/or V2. Separate your answers with a comma. 3. What is the total change…arrow_forward
- Calculate the actual work done on the 200 g mass using W = mgh. Be careful to use only the change in height of the mass. How does this compare to the work done by the gas from step C? Does the gas do any work other than lifting the 200 g mass? The given, instructions, and calculations are all indicated in the image. Kindly right in essay form.arrow_forwardUsing Thermordynamics and Work Theorem 0.5 moles of cinnamaldehyde gas that has an initial volume of ten liters expands under the following conditions: 185°F and 800mmHg external pressure. a. How much work is done? Express your answer in L atm. b. Assuming that the container is cylindrical with a base radius of 10cm and can only expand vertically, how much kinetic energy does a single molecule possesses if it travels from base to base of the expanded cylinder in 10μs? Express your answer in J.arrow_forwardSuppose we are dealing with an ideal gas contained in a cylinder equipped with a movable collection. The gas undergoes different types of thermodynamic transformations while interacting with the environment. Let us consider that the gas undergoes a series of transformations under different conditions of pressure and volume. For all exercises, use the general gas law PV=nRT to perform the calculations and remember to indicate the units correctly. Exercise 1 - Isothermal Transformation:During an isothermal transformation of an ideal gas, where the temperature T is held constant, the initial pressure of the gas is approximately 1250 Pa, and its final pressure is approximately 630 Pa. For ideal gases R is 0.082 atm.L/mol. K, and the temperature T is 300 K, calculate the initial and final volumes (Vi and Vf) at which the gas is during this isothermal transformation.Remember that 1 atm=101325 Pa Please make it typeable, as handwriting hinders understanding.arrow_forward
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