COLLEGE PHYSICS,V.2
COLLEGE PHYSICS,V.2
11th Edition
ISBN: 9781305965522
Author: SERWAY
Publisher: CENGAGE L
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Chapter 10, Problem 44P

A sealed cubical container 20.0 cm on a side contains a gas with three times Avogadro’s number of neon atoms at a temperature of 20.0°C. (a) Find the internal energy of the gas. (b) Find the total translational kinetic energy of the gas. (c) Calculate the average kinetic energy per atom, (d) Use Equation 10.13 to calculate the gas pressure. (e) Calculate the gas pressure using the ideal gas law (Eq. 10.8).

(a)

Expert Solution
Check Mark
To determine
The internal energy of the gas.

Answer to Problem 44P

The internal energy of the gas is 1.1×104J .

Explanation of Solution

Given info: The number of moles (n) is 3. The temperature (T) is 20οC . The side of the cube(r) is 20 cm. Molar mass of neon gas is 20.180×103kg/mol .

Formula to calculate the internal energy of the gas is,

U=32nRT

  • R is the gas constant.

Substitute 3 mol for n, 20οC for T and 8.31Jmol1K1 for R in the above equation to get U.

U=32(3mol)(8.31Jmol1K1)(20οC)=32(3mol)(8.31Jmol1K1)(20+273K)=1.1×104J

Conclusion:

The internal energy of the gas is 1.1×104J .

(b)

Expert Solution
Check Mark
To determine
The total translational kinetic energy of the gas ( (KE)total ).

Answer to Problem 44P

The total translational kinetic energy of the gas is 1.1×104J .

Explanation of Solution

Given info: The number of moles (n) is 3. The temperature (T) is 20οC . The side of the cube(r) is 20 cm. Molar mass of neon gas is 20.180×103kg/mol .

The total translational kinetic energy is equal to the internal energy. Therefore,

(KE)total=U

From (a), U=1.1×104J .

Conclusion:

The internal energy of the gas is 1.1×104J .

(c)

Expert Solution
Check Mark
To determine
The average kinetic energy per atom ( (KE)avg ).

Answer to Problem 44P

The average kinetic energy per atom is 6.07×1021J .

Explanation of Solution

Given info: The number of moles (n) is 3. The temperature (T) is 20οC . The side of the cube(r) is 20 cm. Molar mass of neon gas is 20.180×103kg/mol .

Formula to calculate the average kinetic energy per atom is,

(KE)avg=(KE)totalnNA

  • NA is the Avogadro number.

Substitute 1.1×104J for (KE)total , 3 mol for n and 6.02×1023atoms/mol for NA to get (KE)avg .

(KE)avg=1.1×104J(3mol)(6.02×1023atoms/mol)=6.07×1021J

Conclusion:

The average kinetic energy per atom is 6.07×1021J .

(d)

Expert Solution
Check Mark
To determine
The gas pressure.

Answer to Problem 44P

The gas pressure is 9.14×105Pa .

Explanation of Solution

Given info: The number of moles (n) is 3. The temperature (T) is 20οC . The side of the cube(r) is 20 cm. Molar mass of neon gas is 20.180×103kg/mol .

Formula to calculate the gas pressure is,

P=23(nNAV)(KE)avg (I)

  • V is the volume of the cube.

Formula to calculate the volume of the cube is,

V=r3 (II)

From Equations (I) and (II),

P=23(nNAr3)(KE)avg

Substitute 20 cm for r, 6.07×1021J for (KE)avg , 3 mol for n and 6.02×1023atoms/mol for NA to get P.

P=23[(3mol)(6.02×1023atoms/mol)(20cm)3](6.07×1021J)=23[(3mol)(6.02×1023atoms/mol)(20×102m)3](6.07×1021J)=9.14×105Pa

Conclusion:

The gas pressure is 9.14×105Pa .

(e)

Expert Solution
Check Mark
To determine
The gas pressure.

Answer to Problem 44P

The gas pressure is 9.13×105Pa .

Explanation of Solution

Given info: The number of moles (n) is 3. The temperature (T) is 20οC . The side of the cube(r) is 20 cm. Molar mass of neon gas is 20.180×103kg/mol .

From Ideal gas law, the gas pressure is,

P=nRTV (III)

Formula to calculate the volume of the cube is,

V=r3 (IV)

From Equations (III) and (IV),

P=nRTr3

Substitute 20 cm for r, 3 mol for n 20οC for T and 8.31Jmol1K1 for R to get P.

P=(3mol)(8.31Jmol1K1)(20οC)(20cm)3=(3mol)(8.31Jmol1K1)(20+273K)(20×102m)3=9.13×105Pa

Conclusion:

The gas pressure is 9.13×105Pa .

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Chapter 10 Solutions

COLLEGE PHYSICS,V.2

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