Concept explainers
(a)
The pressure at the center of sun.
Given:
Temperature at the center of the gas is 1 × 10 7 K .
Density at the center of sun is 1 × 10 5 kg / m 3 .
Formula used:
Write the expression for the ideal gas.
P V = n R T
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 = n R T V ........ (1)
Write the expression for the number of moles.
n p = m p M p ........ (2)
Here, n p is the number of moles of protons, m p is the mass of protons and M p is the molar ma of proton.
Calculation:
Substitute 10 5 kg for m p and 10 − 3 kg for M p in equation (2).
n p = 10 5 kg 10 − 3 kg n p = 10 8
The number of electrons is 2 × 10 8 .
Substitute 2 × 10 8 mol for n , 8.314 J / mol ⋅ K for R , 10 7 K for T and 1 m 3 for V in equation (1).
P = ( 2 × 10 8 ) ( 8.314 J / mol ⋅ K ) 10 7 K 1 m 3 P = 2 × 10 11 atm
Conclusion:
The pressure is 2 × 10 11 atm .
The pressure at the center of sun.
Given:
Temperature at the center of the gas is
Density at the center of sun is
Formula used:
Write the expression for the ideal gas.
Here,
Solve the above equation for
Write the expression for the number of moles.
Here,
Calculation:
Substitute
The number of electrons is
Substitute
Conclusion:
The pressure is
(a)
Explanation of Solution
Given:
Temperature at the center of the gas is
Density at the center of sun is
Formula used:
Write the expression for the ideal gas.
Here,
Solve the above equation for
Write the expression for the number of moles.
Here,
Calculation:
Substitute
The number of electrons is
Substitute
Conclusion:
The pressure is
(b)
The root mean square speed of electron and proton at the center of the sun.
(b)
Explanation of Solution
Given:
TheTemperature at the center of the gas is
Formula used:
Write the expression for the root mean square speed of the molecule.
Here,
Calculation:
Substitute
Substitute
Conclusion:
The rms speed of proton and electron at the center of sun is
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Chapter 17 Solutions
Physics For Scientists And Engineers
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