Physics for Scientists and Engineers
Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 17, Problem 29P

(a)

To determine

The pressure at the center of sun.

Given:

Temperature at the center of the gas is 1×107K .

Density at the center of sun is 1×105kg/m3 .

Formula used:

Write the expression for the ideal gas.

  PV=nRT

Here, P is the pressure, V is the volume, n is the number of moles, R is the gas constant and T is the temperature.

Solve the above equation for P .

  P=nRTV ........ (1)

Write the expression for the number of moles.

  np=mpMp ........ (2)

Here, np is the number of moles of protons, mp is the mass of protons and Mp is the molar ma of proton.

Calculation:

Substitute 105kg for mp and 103kg for Mp in equation (2).

  np= 105kg 10 3kgnp=108

The number of electrons is 2×108 .

Substitute 2×108mol for n , 8.314J/molK for R , 107K for T and 1m3 for V in equation (1).

  P=( 2× 10 8 )( 8.314J/ molK ) 107K1m3P=2×1011atm

Conclusion:

The pressure is 2×1011atm .

(a)

Expert Solution
Check Mark

Explanation of Solution

Given:

Temperature at the center of the gas is 1×107K .

Density at the center of sun is 1×105kg/m3 .

Formula used:

Write the expression for the ideal gas.

  PV=nRT

Here, P is the pressure, V is the volume, n is the number of moles, R is the gas constant and T is the temperature.

Solve the above equation for P .

  P=nRTV ........ (1)

Write the expression for the number of moles.

  np=mpMp ........ (2)

Here, np is the number of moles of protons, mp is the mass of protons and Mp is the molar ma of proton.

Calculation:

Substitute 105kg for mp and 103kg for Mp in equation (2).

  np= 105kg 10 3kgnp=108

The number of electrons is 2×108 .

Substitute 2×108mol for n , 8.314J/molK for R , 107K for T and 1m3 for V in equation (1).

  P=( 2× 10 8 )( 8.314J/ molK ) 107K1m3P=2×1011atm

Conclusion:

The pressure is 2×1011atm .

(b)

To determine

The root mean square speed of electron and proton at the center of the sun.

(b)

Expert Solution
Check Mark

Explanation of Solution

Given:

TheTemperature at the center of the gas is 1×107K .

Formula used:

Write the expression for the root mean square speed of the molecule.

  vrms=3kTM ........ (1)

Here, vrms is the root mean square speed of the molecule, k is the Boltzmann constant, T is the temperature and M is the molar mass of the molecule.

Calculation:

Substitute 8.314J/molK for R , 107K for T and 0.001kg for M in equation (1)

  vrms= 3( 8.314J/ molK )( 10 7 K ) 0.001kgvrms=5×105m/s

Substitute 8.314J/molK for R , 107K for T and 12000(0.001kg) for M in equation (1).

  vrms= 3( 8.314J/ molK )( 10 7 K ) 1 2000 ( 0.001kg )vrms=2×107m/s

Conclusion:

The rms speed of proton and electron at the center of sun is 5×105m/s and 2×107m/s respectively.

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