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Check Your Understandin g The quantities below represent four different transitions between the same initial and final state. Fill in the blanks.

Q (J) W (J) Δ E int ( J )
–80 –120
90
40
–40

Line 1, Δ E int = 40 J; line 2, W = 50 J and Δ E int = 40 J; line 3, Q = 80 J and Δ E int = 40 J; and line 4, Q = 0 and Δ E int = 40 J

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An ideal gas making transitions between two states

Consider the quasi-static expansions of an ideal gas between the equilibrium states A and C of [link] . If 515 J of heat are added to the gas as it traverses the path ABC , how much heat is required for the transition along ADC ? Assume that p 1 = 2.10 × 10 5 N/m 2 , p 2 = 1.05 × 10 5 N/m 2 , V 1 = 2.25 × 10 −3 m 3 , and V 2 = 4.50 × 10 −3 m 3 .

Strategy

The difference in work done between process ABC and process ADC is the area enclosed by ABCD . Because the change of the internal energy (a function of state) is the same for both processes, the difference in work is thus the same as the difference in heat transferred to the system.

Solution

For path ABC , the heat added is Q A B C = 515 J and the work done by the gas is the area under the path on the pV diagram, which is

W A B C = p 1 ( V 2 V 1 ) = 473 J .

Along ADC , the work done by the gas is again the area under the path:

W A D C = p 2 ( V 2 V 1 ) = 236 J .

Then using the strategy we just described, we have

Q A D C Q A B C = W A D C W A B C ,

which leads to

Q A D C = Q A B C + W A D C W A B C = ( 515 + 236 473 ) J = 278 J .

Significance

The work calculations in this problem are made simple since no work is done along AD and BC and along AB and DC ; the pressure is constant over the volume change, so the work done is simply p Δ V . An isothermal line could also have been used, as we have derived the work for an isothermal process as W = n R T ln V 2 V 1 .

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Isothermal expansion of an ideal gas

Heat is added to 1 mol of an ideal monatomic gas confined to a cylinder with a movable piston at one end. The gas expands quasi-statically at a constant temperature of 300 K until its volume increases from V to 3 V . (a) What is the change in internal energy of the gas? (b) How much work does the gas do? (c) How much heat is added to the gas?

Strategy

(a) Because the system is an ideal gas, the internal energy only changes when the temperature changes. (b) The heat added to the system is therefore purely used to do work that has been calculated in Work, Heat, and Internal Energy . (c) Lastly, the first law of thermodynamics can be used to calculate the heat added to the gas.

Solution

  1. We saw in the preceding section that the internal energy of an ideal monatomic gas is a function only of temperature. Since Δ T = 0 , for this process, Δ E int = 0 .
  2. The quasi-static isothermal expansion of an ideal gas was considered in the preceding section and was found to be
    W = n R T ln V 2 V 1 = n R T ln 3 V V = ( 1.00 mol ) ( 8.314 J/K · mol ) ( 300 K ) ( ln 3 ) = 2.74 × 10 3 J .
  3. With the results of parts (a) and (b), we can use the first law to determine the heat added:
    Δ E int = Q W = 0 ,

    which leads to
    Q = W = 2.74 × 10 3 J .

Significance

An isothermal process has no change in the internal energy. Based on that, the first law of thermodynamics reduces to Q = W .

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Check Your Understanding Why was it necessary to state that the process of [link] is quasi-static?

So that the process is represented by the curve p = n R T / V on the pV plot for the evaluation of work.

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Questions & Answers

Newton's second laws is call with
Dyutee Reply
Really
Arzoodan
what is mean by thermodynamics
Prasad Reply
it is study about temperature and it's equilibrium
thiru
Its the study of heat and its relation with others kind of energy
Antonio
state caulombs law clearly
constand Reply
show mathematically that an electron has the greater speed than the proton when they attract each other
ezra Reply
show mathematically that an electron has the greater speed than the proton when they attract each other
srikanta
@ezra & srikanta; for electrons: a=ke^2/(mr^2) and for protons: a=kp^2/(mr^2)
Sikandar
what is electrostatics
Hero Reply
the study of charge at rest
Gulzar
@Hero; the study of charges at rest is the electrostatics
Sikandar
okay what is electrostatic?
Abd
charge at rest
Nawal
set of character...
Arzoodan
oky
Abd
Gauss law, electric fields, dipoles,...
Antonio
good
Abd
A proton initially at rest falls through a p.d of 25000V. what speed does it gain?
Minister Reply
@Minister; use equation v= sq root(2×eV/m)
Sikandar
what is the reaction of heat on magnet
ORIZINO Reply
Magnetization decreases with increase in temperature. But in case of diamagnetic substance heat has no role on magnetization.
srikanta
what is a physical significant of electric dipole moment .
PRANAB Reply
A dipole moment it's a mechanical electrical effect used in nature
Antonio
what is the uses of carbon brushes in generator
Malik Reply
to minimize heat
constand
at what temperature is the degree Fahrenheit equal to degree Celsius
Grace Reply
Celsius and Faharaneith are different, never equal
Antonio
find their liners express of n=a+b/T² ( plot graph n against T)
Donsmart Reply
Radio Stations often advertis "instant news,,if that meens you can hear the news the instant the radio announcer speaks it is the claim true? what approximate time interval is required for a message to travel from Cairo to Aswan by radio waves (500km) (Assume the waves Casbe detected at this range )
mahmod Reply
what is growth and decay
Pawan Reply
Can someone please predict the trajectory of a point charge in a uniform electric field????
erlinda Reply
what is deference between strong force and coulomb force
zahid Reply
how do you convert temperature in degree Celsius to Fahrenheit
kwame
Celsius x 9/5 +32
Cyclone
Practice Key Terms 1

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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