Essential University Physics, 3e (Wolfson) Chapter 18 Heat, Work, Work, and the First Law of Thermodynamics
1 8. 1 Co nc e pt ua lQue s t i o ns 1) When a gas undergoes an isothermal process, there is A) no change in the pressure of the gas. B) no change in the temperature of the gas. C) no change in the volume of the gas. D) no work done b !or on) the gas. ") no heat added to the gas. Answer# B $ar# 1
%) An ideal gas is compressed in a well&insulated chamber using a well&insulated piston. 'his process is A) isochoric. B) isothermal. C) adiabatic. D) isobaric. Answer# C $ar# 1
() 'he process shown in the T-V diagram in the figure is an
A) adiabatic compression. B) isothermal compression. C) isochoric compression. D) isobaric compression. ") isothermal epansion. Answer# B $ar# 1
1 Copright * %+1 -earson "ducation, nc.
/) 'he process shown in the pV diagram in the figure is an
A) adiabatic epansion. B) isothermal epansion. C) isochoric epansion. D) isobaric epansion. ") isochoric compression. Answer# D $ar# 1
0) 'he process shown in the pV diagram in the figure is
A) adiabatic. B) isothermal. C) isochoric. D) isobaric. Answer# C $ar# 1
% Copright * %+1 -earson "ducation, nc.
) Consider two clinders of gas identical in all respects ecept that one contains ogen % and the other helium 2e. Both clinders initiall contain the same volume of gas at +3C and 1 atm of pressure and are closed b a movable piston at one end. Both gases are now compressed adiabaticall to one&third their original volume. !a) Which gas will show the greater temperature increase4 A)the % B) the 2e C) 5either6 both will show the same increase. D) t is impossible to tell from the information given. !b) Which gas will show the greater pressure increase4 A)the % B) the 2e C) 5either6 both will show the same increase. D) t is impossible to tell from the information given. Answer# !a) B !b) B $ar# 1
7) When a fied amount of ideal gas goes through an isothermal epansion A) its internal !thermal) energ does not change. B) the gas does no work. C) no heat enters or leaves the gas. D) its temperature must decrease. ") its pressure must increase. Answer# A $ar# 1
8) When a fied amount of ideal gas goes through an adiabatic epansion A) its internal !thermal) energ does not change. B) the gas does no work. C) no heat enters or leaves the gas. D) its temperature cannot change. ") its pressure must increase. Answer# C $ar# 1
9) When a fied amount of ideal gas goes through an isobaric epansion A) its internal !thermal) energ does not change. B) the gas does no work. C) no heat enters or leaves the gas. D) its temperature must increase. ") its pressure must increase. Answer# D $ar# 1
( Copright * %+1 -earson "ducation, nc.
1+) When a fied amount of ideal gas goes through an isochoric process A) its internal !thermal) energ does not change. B) the gas does no work. C) no heat enters or leaves the gas. D) its temperature must increase. ") its pressure must increase. Answer# B $ar# 1
11) An ideal gas increases in temperature from %%3C to /%3C b two different processes. n one process, the temperature increases at constant volume, and in the other process the temperature increases at constant pressure. Which of the following statements about this gas are correct4 !'here ma be more than one correct choice.) A) 'he heat re:uired to cause this temperature change is the same for both the constant&volume and the constant&pressure processes. B) ;ore heat is re:uired for the constant&pressure process than for the constant&volume process. C) 'he change in the internal !thermal) energ of the gas is the same for both the constant& volume and the constant&pressure processes. D) 'he root&mean&s:uare !thermal) speed of the gas molecules increases more during the constant&volume process than during the constant&pressure process. Answer# B, C $ar# 1
1%) A container of ideal gas has a movable frictionless piston. 'his container is placed in a ver large water bath and slowl compressed so that the temperature o f the gas remains constant and e:ual to the temperature of the water. Which of the following statements about this gas are true for this process4 !'here ma be more than one correct choice.) A) 2eat leaves the gas during the compression. B)
1() When an ideal gas increases in volume at constant pressure, the average kinetic energ of the gas molecules A) increases. B) decreases. C) does not change. D) ma either increase or decrease, depending on whether or not the process is carried out adiabaticall. ") ma or ma not change, but insufficient information is given to make such a determination. Answer# A $ar# 1 / Copright * %+1 -earson "ducation, nc.
1 8 . 2 Pr o bl e ms 1) 'he figure !not to scale) shows a pV diagram for 1.8 g of helium gas !2e) that undergoes the process 1 = % = (. >ind the value of V (. 'he ideal gas constant is R ? 8.(1/ @mol ? +.+8%1 atmmol , and the atomic weight of helium is /.+ gmol.
A) 17 B) 9 C) (/ D) 8. Answer# A $ar# 0+E
0 Copright * %+1 -earson "ducation, nc.
%) 'he figure shows a pV diagram for 8.( g of nitrogen gas !5 %) in a sealed container. 'he temperature T 1 of the gas in state 1 is 793C. What are !a) the pressure p1 of the gas in state 1 and !b) the temperature T % of the gas in state %4 'he ideal gas constant is R ? 8.(1/ @mol ? +.+8%1 atmmol , and the A';C weight of nitrogen is 1/ gmol.
A) !a) 8 atm, !b) 7++3C. B) !a) 19 atm, !b) 7++3C. C) !a) 8 atm, !b) 1+3C. D) !a) 19 atm, !b) 1+3C. Answer# A $ar# 0+E
Copright * %+1 -earson "ducation, nc.
() 'he figure shows a pV diagram for /.( g of ogen gas !%) in a sealed container. 'he temperature T 1 of the gas in state 1 is %13C. What are the temperatures T ( and T / of the gas in states ( and /4 'he ideal gas constant is R ? 8.(1/ @mol ? +.+8%1 atmmol , and the A';C weight of ogen is 1 gmol.
A) &0%3C, (9+3C B) 13C, /73C C) %%+3C, +3C D) 113C, (%3C Answer# A $ar# 0+E
7 Copright * %+1 -earson "ducation, nc.
/) 'he figure shows a pV diagram for +.90 mol of gas that undergoes the process 1 = %. 'he ga s then undergoes an isochoric heating from point % until the pressure is restored to the value it had at point 1. What is the final temperature of the gas4 'he ideal gas constant is R ? 8.(1/ @mol ? +.+8%1 atmmol .
A) &1+3C B) 103C C) (9+3C D) 1%+3C Answer# A $ar# 0+E
8 Copright * %+1 -earson "ducation, nc.
0) 'he figure shows a pV diagram for +.++ mol of gas that undergoes the process 1 = % = (. What is the pressure p%. 'he ideal gas constant is R ? 8.(1/ @mol ? +.+8%1 atmmol .
A) 0.( atm B) 0.( F 1+0 atm C) 1 atm D) 1. F 1+ atm Answer# A $ar# (+
) 2ow much work is done b (.++ mol of ideal gas when it triples its volume at a constant temperature of 1%73C4 'he ideal gas constant is R ? 8.(1/ @mol . A) 1%.7 k@ B) 9.97 k@ C) 11.+ k@ D) 10.( k@ ") 1.%+ k@ Answer# C $ar# 1
7) An ideal gas in a balloon is kept in thermal e:uilibrium with its constant&temperature surroundings. 2ow much work is done b the gas if the outside pressure is slowl reduced, allowing the balloon to epand to .+ times its original siGe4 'he balloon initiall has a pressure of and a volume of 'he ideal gas constant is R ? 8.(1/ @mol . A) 1%+ @ B) (9+ @ C) &((+ @ D) .+ @ Answer# A $ar# 0+E 9 Copright * %+1 -earson "ducation, nc.
8) A steel container, e:uipped with a piston, contains %1 mol of an ideal gas at /0 . 'he container is compressed isothermall to 9+H of its original volume. 2ow much work is done on the gas4 'he ideal gas constant is R ? 8.(1/ @mol . A) 8++ @ B) &7(,(++ @ C) &80++ @ D) 11 @ Answer# A $ar# 1
9) A certain amount of ideal monatomic gas is maintained at constant volume as it is cooled from /00 to /+0 . 'his feat is accomplished b removing /++ @ of heat from the gas. 2ow much work is done b the gas during this process4 'he ideal gas constant is R ? 8.(1/ @mol . A) +.++ @ B) %++ @ C) /++ @ D) &/++ @ ") &%++ @ Answer# A $ar# 1
1+) An ideal monatomic gas cools from /00.+ to /+0.+ at constant volume as 8(1 @ of energ is removed from it. 2ow man moles of gas are in the sample4 'he ideal gas constant is R ? 8.(1/ @mol . A) %.0+ mol B) %.10 mol C) 1.0+ mol D) 1.(( mol ") +.7%0 mol Answer# D $ar# 1
11) (.+ moles of an ideal gas with a molar h eat capacit at constant volume of /.9 cal!mol) and a molar heat capacit at constant pressure of .9 cal!mol) starts at (++ and is heated at constant pressure to (%+ , then cooled at constant volume to its original temperature. 2ow much heat flows into the gas during this two&step process4 A) 71+ cal B) &7%+ cal C) +.++ cal D) 1%+ cal ") &1%+ cal Answer# D $ar# 1
1+ Copright * %+1 -earson "ducation, nc.
1%) A :uantit of ideal gas re:uires 8++ k@ to raise the temperature of the gas b 1+.+ when the gas is maintained at constant volume. 'he same :uantit of gas re:uires 9++ k@ to raise the temperature of the gas b 1+.+ when the gas is maintained at constant pressure. What is the adiabatic constant γ for this gas4 A) +.889 B) 1.1( C) 1.%% D) 1.7 ") 1./+ Answer# B $ar# 1
1() 'he temperature of an ideal gas in a sealed +./+&
rigid container is reduced from (0+ to
'he final pressure of the gas is 'he molar heat capacit at constant volume of the gas is %8.+ @mol . 'he heat absorbed b the gas is closest to A) &%/ k@. B) &(1 k@. C) %/ k@. D) (1 k@. ") +.++ k@. Answer# A $ar# 0+E
1/) 'he temperature of an ideal gas in a sealed +./+
container is reduced from /++ to
'he final pressure of the gas is 'he molar heat capacit at constant volume of the gas is %8.+ @mol . 'he work done b the gas is closest to A) +.++ k@. B) &19 k@. C) &%0 k@. D) 19 k@. ") %0 k@. Answer# A $ar# 0+E
10) A compression, at a constant pressure of 19+ k-a, is performed on 0.+ moles of an ideal monatomic gas. 'he compression reduces the volume of the gas from
to
ideal gas constant is R ? 8.(1/ @mol . 'he work done b the gas is closest to A) &1( k@. B) 1( k@. C) &(( k@. D) (( k@. ") +.++ k@. Answer# A $ar# 0+E
11 Copright * %+1 -earson "ducation, nc.
'he
1) A monatomic ideal gas undergoes an isothermal epansion at (++ , as the volume increased from
to
'he final pressure of the gas is
'he ideal gas constant is R ?
8.(1/ @mol . 'he change in the internal !thermal) energ of the gas is closest to A) +.++ k@. B) 1% k@. C) %0 k@. D) &1% k@. ") &%0 k@. Answer# A $ar# 0+E
17) A monatomic ideal gas undergoes an isothermal epansion at (++ , as the volume increased from
to
'he final pressure is
'he ideal gas constant is R ? 8.(1/
@mol . 'he heat transfer to the gas is closest to A) (.( k@. B) 1.7 k@. C) &(.( k@. D) &1.7 k@. ") +.++ k@. Answer# A $ar# 0+E
18) An epansion process on an ideal diatomic gas has a linear path between the initial and final states on a pV diagram. 'he initial pressure is
the initial volume is
and the
initial temperature is 'he ideal gas constant is R ? 8.(1/ @mol . 'he final pressure is and the final temperature is 'he work done b the gas is closest to A) /0++ @. B) %(++ @. C) (/++ @. D) 0++ @. ") 8++ @. Answer# A $ar# 0+E
19) An epansion process on an ideal diatomic gas has a linear path between the initial and final states on a pV diagram. 'he initial pressure is
the initial volume is
initial temperature is 'he final pressure is and the final temperature is 'he change in the internal !thermal) energ of the gas is closest to A) &(1++ @. B) &18++ @. C) (1++ @. D) 18++ @. ") +.++ @. Answer# A $ar# 0+E
1% Copright * %+1 -earson "ducation, nc.
and the
%+) An adiabatic compression is performed on an ideal gas. 'he final pressure is e:ual to +.0+ times the initial pressure and the final volume e:uals 1.0+ times the initial volume. What is the adiabatic constant for the gas4 A) 1.(( B) 1./( C) 1./8 D) 1.0% ") 1.7 Answer# B $ar# 1
%1) An ideal gas with I ? 1.7 is initiall at +3C in a volume of 1+.+ at a pressure of 1.++ atm. t is then epanded adiabaticall to a volume of 1+./ . What is the final temperature of the gas4 A) &7.13C B) %.03C C) &%(3C D) 83C ") &%+3C Answer# A $ar# 1
%%) During an isothermal process, 0.+ @ of heat is removed from an ideal gas. What is the change in internal !thermal) energ of the gas4 A) +.++ @ B) %.0 @ C) 0.+ @ D) 7.0 @ ") 1+ @ Answer# A $ar# 1
%() During an isothermal process, 0.+ @ of heat is removed from an ideal gas. 2ow much work does the gas do during this process4 A) +.++ @ B) %.+ @ C) 0.+ @ D) &0.+ @ ") 1+ @ Answer# D $ar# 1
1( Copright * %+1 -earson "ducation, nc.
%/) During an adiabatic process, an ideal gas does %0 @ of work. What is the change in the internal !thermal) energ of the gas during this process4 A) +.++ @ B) 0+ @ C) %0 @ D) &%0 @ ") &0+ @ Answer# D $ar# 1
%0) n an isochoric process, the internal !thermal) energ of an ideal gas decreases b 0+ @. 2ow much work does the gas do during this process4 A) +.++ @ B) %0 @ C) 0+ @ D) &%0 @ ") &0+ @ Answer# A $ar# 1
%) n an isochoric process, the internal !thermal) energ of an ideal gas decreases b 0+ @. 2ow much heat is echanged with the gas during this process4 A) +.++ @ B) %0 @ C) 0+ @ D) &%0 @ ") &0+ @ Answer# " $ar# 1
%7) A sstem has a heat source suppling heat to an ideal gas at a rate of 187.+ W and the gas is doing work at a rate of 1(+.9 W. At what rate is the internal !thermal) energ of the gas changing4 A) 0.1 W B) (18 W C) &0.1 W D) 187 W Answer# A $ar# 1
%8) 'he gas in a perfectl insulated sstem does work at a rate of internal !thermal) energ of the gas changing4 A) &1( W B) 1( W C) +.++ W D) .0 W Answer# A $ar# 0+E 1/ Copright * %+1 -earson "ducation, nc.
At what rate is the
%9) An ideal gas is allowed to epand slowl at constant temperature to twice its original volume. During the epansion, the gas absorbs %++ k@ of heat. !a) What is the change in the internal !thermal) energ of the gas during the epansion4 !b) 2ow much work does the gas do during the epansion4 Answer# !a) Gero !b) %++ k@ $ar# 1
(+) An ideal gas initiall at (++ and occuping a volume of %+ is adiabaticall compressed. f its final temperature is /++ and γ ? 1.(+, what is its final volume4 A) 7.7 B) 1/ C) %% D) 0% Answer# A $ar# 1
(1) A container with rigid walls is filled with / mol of air with C $ ? %.0 R. 2ow much does the internal !thermal) energ change if the temperature of the air rises from 13C to /(73C4 'he ideal gas constant is R ? 8.(1/ @mol . A) (0 k@ B) /%1 @ C) (.0 k@ D) 8.70 k@ Answer# A $ar# 1
(%) An ideal gas with γ ? 1.(+ occupies 7.+ at (++ and %++ k-a pressure. t is compressed adiabaticall to 17 of its original volume, then c ooled at constant volume to (++ , and finall allowed to epand isothermall to 7.+ . 2ow much work does the gas do during this process4 'he ideal gas constant is R ? 8.(1/ @mol ? +.+8%1 atmmol . A) &98+ @ B) /++ @ C) &%7+,+++ @ D) &/++ @ ") 98+ @ Answer# A $ar# 1
10 Copright * %+1 -earson "ducation, nc.
(() 'he pV diagram shown is for 7.0+ moles of an ideal diatomic gas taken through a ccle from a to b to c. 'he ideal gas constant is R ? 8.(1/ @mol .
!a) What is the highest temperature reached b the gas during the ccle4 !b) What net work does the gas do during the ccle4 !c) 2ow much heat is echanged with the gas during part bc of the ccle4 Does it enter or leave the gas4 !d) What is the change in the internal !thermal) energ of the gas during part bc of the ccle4 !e) What is the change in the internal !thermal) energ of the gas during the entire ccle4 Answer# !a) %+83C !b) /.++ k@ !c) (+.+ k@, leaves the gas !d) &(+.+ k@ !e) +.++ @ $ar# 1
(/) A clinder contains %( moles of an ideal gas at a temperature of (++ . 'he gas is compressed at constant pressure until the final volume e:uals +./ ( times the initial volume. 'he molar heat capacit at constant volume of the gas is %/.+ @mol and the ideal gas constant is R ? 8.(1/ @mol . 'he heat absorbed b the gas is closest to A) &1(+ k@. B) &9/ k@. C) 1(+ k@. D) 9/ k@. ") &(( k@. Answer# A $ar# 0+E
1 Copright * %+1 -earson "ducation, nc.
(0) A clinder contains %/.+ moles of an ideal gas at a temperature of (++ . 'he gas is compressed at constant pressure until the final volume e:uals +. ( times the initial volume. 'he molar heat capacit at constant volume of the gas is %/.+ @mol and the ideal gas constant is R ? 8.(1/ @mol . 'he change in the internal !thermal) energ of the gas is closest to A) &/ k@. B) &8 k@. C) / k@. D) 8 k@. ") &%% k@. Answer# A $ar# 0+E
() During an adiabatic process, %+ moles of a monatomic ideal gas undergo a temperature change from /0+ to (%+ starting from an initial pressure is /++ k-a. 'he ideal gas constant is R ? 8.(1/ @mol . !a) What is the final volume of the gas4 !b) 2ow much heat does the gas echange during this process4 !c) What is the change in the internal !thermal) energ of the gas during this process4 Answer# !a) +.(1 m( !b) +.++ @ !c) &(% k@ $ar# 1
(7) 'he figure shows the pV diagram for a certain thermodnamic process. n this process, 10++ @ of heat flows into a sstem, and at the same time the sstem epands against a constant eternal pressure of
f the volume of the sstem increases from
to
calculate the change in internal !thermal) energ of the sstem. f the internal !thermal) energ change is nonGero, be sure to indicate whether this energ change is positive or negative.
Answer# E&1%++ @ $ar# 0+E
17 Copright * %+1 -earson "ducation, nc.
(8) A fied amount of ideal gas goes through a process abc. n state a, the temperature of the gas is 10%3C, its pressure is 1.%0 atm, and it occupies a volume of +.%0+ m(. t then undergoes an isothermal epansion to state b that doubles its volume, followed b an isobaric compression back to its original volume at state c. ! Hint: >irst show this process on a pV diagram.) 'he ideal gas constant is 8.(1/ @mol , and 1.++ atm ? 1.+1 F 1+0 -a. !a) 2ow man moles does this gas contain4 !b) What is the change in the internal energ of the gas between states a and b4 !c) What is the net work done on !or b) this gas during the entire process4 !d) What is the temperature of the gas in state c4 Answer# !a) 8.9( moles !b) +.++ @ !c) .1+ F 1+( @ !d) %1( $ar# 1
(9) A clinder contains 1.% moles of ideal gas, initiall at a temperature of 113C. 'he clinder is provided with a frictionless piston, which maintains a constant pressure of gas. 'he gas is cooled until its temperature has decreased to
on the
>or the gas
and the ideal gas constant !a) >ind the work done b !or on) the gas during this process. s the work done b or on the gas4 !b) What is the change in the internal !thermal) energ of the gas during this process4 !c) 2ow much heat is transferred to !or from) the gas d uring this process4 Does this heat flow into or out of the gas4 Answer# !a) W ? &89+ @ !the negative sign means that work is done on the gas) !b) &1%++ @ !c) Q ? &%1++ @ !the negative sign means that heat flows out of the gas) $ar# 0+E
/+) n a thermodnamic process involving 7.8 moles of an ideal gas, the gas is at an initial temperature of %/3C and has an initial volume of +.+/+ m(. 'he gas epands adiabaticall to a volume of +.+8+ m(. >or this gas, C $ ? 1%.%7 @mol , and the ideal gas constant is R ? 8.(1/ @mol . Calculate the work done b the gas during this epansion. Answer# 11 k@ $ar# 1
18 Copright * %+1 -earson "ducation, nc.
