A dilute gas expands quasi-statically from 0.3 to 4.3 L at a constant temperature of 290 K. Follow the steps below to calculate the number of molecules in the gas, with some additional information provided. Hint For an isothermal expansion, does the pressure of the gas remain constant? Hint for (a) Answer depends on additional information not given. Yes, it remains constant. No, it does not remain constant. Correct If the pressure does not remain constant, we cannot calculate the whole amount of work with W=PΔVW=PΔV. Instead, we need to start out with the infinitesimal work done for infinitesimal volume change (dW=PdVdW=PdV) and integrate over the interval of volume change to calculate the total work done (this is also same as the area under the curve in P-V diagram). Fill in the blank in the setup for the integral below, in terms of VV (volume), NN (number of molecules), TT (temperature), and kk (Boltzmann constant) and other numerical constants. Hint for (b) Total work done in volume change from ViVi to VfVf is, W=∫VfViW=∫ViVfPdVIncorrect syntax error. Check your variables - you might be using an incorrect one. dVdV. Complete the integral above and write down work done in terms of ViVi, VfVf, NN, TT, kk, and other numerical constants. Hint for (c) Total work done in volume change from ViVi to VfVf is, W=W=3.20E−18Incorrect . (Format hint: Subscripts are typed using underscores. For example, to type ViVi, type in "V_i". Natural logs are represented with function "ln". That is, for "natural log of 12", for example, type in "ln(12)".) Suppose that amount of 400 J of work was done in this expansion. Find the value of NN (that is, how many molecules are in this gas?). Hint for (d) N=N=Correct. (Format Hint: Use the "E" notation to enter numbers in scientific notation. For example, 3.14×10123.14×1012 can be written as "3.14E12".)

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter20: Kinetic Theory Of Gases

Section: Chapter Questions

Problem 66PQ

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Question

A dilute gas expands quasi-statically from 0.3 to 4.3 L at a constant temperature of 290 K. Follow the steps below to calculate the number of molecules in the gas, with some additional information provided.

Hint

For an isothermal expansion, does the pressure of the gas remain constant?

Hint for (a)
- Answer depends on additional information not given.
- Yes, it remains constant.
- No, it does not remain constant.
Correct
If the pressure does not remain constant, we cannot calculate the whole amount of work with W=PΔVW=PΔV. Instead, we need to start out with the infinitesimal work done for infinitesimal volume change (dW=PdVdW=PdV) and integrate over the interval of volume change to calculate the total work done (this is also same as the area under the curve in P-V diagram).

Fill in the blank in the setup for the integral below, in terms of VV (volume), NN (number of molecules), TT (temperature), and kk (Boltzmann constant) and other numerical constants.

Hint for (b)

Total work done in volume change from ViVi to VfVf is,
W=∫VfViW=∫ViVfPdVIncorrect syntax error. Check your variables - you might be using an incorrect one. dVdV.
Complete the integral above and write down work done in terms of ViVi, VfVf, NN, TT, kk, and other numerical constants.

Hint for (c)

Total work done in volume change from ViVi to VfVf is,
W=W=3.20E−18Incorrect .
(Format hint: Subscripts are typed using underscores. For example, to type ViVi, type in "V_i". Natural logs are represented with function "ln". That is, for "natural log of 12", for example, type in "ln(12)".)
Suppose that amount of 400 J of work was done in this expansion. Find the value of NN (that is, how many molecules are in this gas?).

Hint for (d)

N=N=Correct.
(Format Hint: Use the "E" notation to enter numbers in scientific notation. For example, 3.14×10123.14×1012 can be written as "3.14E12".)

Submit QuestionQuestion 2

A dilute gas expands quasi-statically from 0.3 to 4.3 Lat a constant temperature of 290 K. Follow the steps
below to calculate the number of molecules in the gas, with some additional information provided.
Hint
a. For an isothermal expansion, does the pressure of the gas remain constant?
Hint for (a)
Answer depends on additional information not given.
O Yes, it remains constant.
No, it does not remain constant.
b. If the pressure does not remain constant, we cannot calculate the whole amount of work with
W = PAV. Instead, we need to start out with the infinitesimal work done for infinitesimal volume
change (dW = PdV) and integrate over the interval of volume change to calculate the total work
done (this is also same as the area under the curve in P-V diagram).
Fill in the blank in the setup for the integral below, in terms of V (volume), N (number of
molecules), T (temperature), and k (Boltzmann constant) and other numerical constants.
Hint for (b)
Total work done in volume change from V; to V; is,
W
PaV
x syntax error. Check your variables - you might be using
an incorrect one. dV.
c. Complete the integral above and write down work done in terms of Vi, V7, N, T, k, and other
numerical constants.
Hint for (c)
Total work done in volume change from Vị to V; is,
W = 3.20E - 18
(Format hint: Subscripts are typed using underscores. For example, to type Vi, type in "V_i". Natural
logs are represented with function "In". That is, for "natural log of 12", for example, type in "In(12)".)
d. Suppose that amount of 400 J of work was done in this expansion. Find the value of N (that is, how
many molecules are in this gas?).
Hint for (d)
3.75E22
(Format Hint: Use the "E" notation to enter numbers in scientific notation. For example, 3.14 x 1012
can be written as "3.14E12".)
N

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