Concept explainers
(a)
The temperature at which the root mean square speeds for
(a)
Explanation of Solution
Given:
The escape speed of the surface of the planet is
Formula used:
Write the expression for the rms speed of the molecule.
Here,
Equate
Here,
Solve the above equation for
Calculation:
Substitute
Conclusion:
The temperature is
(b)
The temperature at which the root mean square speeds for
(b)
Explanation of Solution
Given:
The escape speed of the surface of the planet is
Formula used:
Write the expression for the rms speed of the molecule.
Here,
Calculation:
Substitute
Conclusion:
The temperature is
(c)
The reason for the low hydrogen in the earth atmosphere.
(c)
Explanation of Solution
Given:
The escape speed of the surface of the planet is
Introduction:
All the giant planets like Jupiter, Saturn, Uranus and Neptune contains helium and hydrogen in the atmosphere of the giant planets.
Earth contains low amount of hydrogen in the atmosphere because hydrogen gas is very light as compared to other elements and has high escape speed at the high temperature and thus hydrogen gas escapes from the earth’s atmosphere.
Conclusion:
The hydrogen gas molecules attain greater escape speed than other elements and therefore earth’s atmosphere contains low amount of hydrogen.
(d)
(d)
Explanation of Solution
Given:
The escape speed of the surface of the planet is
Gravity on moon is one-sixth the gravity on moon.
Radius of earth is
Formula used:
Substitute
Substitute
Here,
Calculation:
Substitute
Thus, the temperature of
Substitute
Conclusion:
The escape speed is low on moon as the acceleration due to gravity is less there. Thus the largerpercentage of molecules moves with escape speed.
Want to see more full solutions like this?
Chapter 17 Solutions
Physics for Scientists and Engineers
- (a) In the deep space between galaxies, me density of atoms is as low as 106atoms/m3, and me temperature is a frigid 2.7 K. What is me pressure? (b) What volume (in m3) is occupied by 1 mol of gas? (c) If this volume is a cube, what is the length of its sides in kilometers?arrow_forwardIf a certain amount of ideal gas occupies a volume at STP on earth, what would be its volume (in terms of V) on Venus, where the temperature is 1003°C and tye pressure is 92 atm?arrow_forwardHow many molecules are in a typical object, such as gas in a tire or water in a drink? We can use the ideal gas law to give us an idea of how large N typically is.Calculate the number of molecules in a cubic meter of gas at standard temperature and pressure (STP), which is defined to be 0ºC and atmospheric pressure.arrow_forward
- The escape velocity of any object from Earth is 11.2 km/s. (a) Express this speed in m/s and km/h. Speed, m/s: Speed, km/h: (b) At what temperature would oxygen molecules (molecular mass is equal to 32 g/mol) have an average velocity, vms, equal to Earth's escape velocity 11.2 km/s?arrow_forwardThe number density of gas atoms at a certain location in the space above our planet is about 1.40 ✕ 1011 m−3, and the pressure is 1.10 ✕ 10−10 N/m2 in this space. What is the temperature (in °C) there?arrow_forwardThe number density of gas atoms at a certain location in the space above our planet is about 1.00×1011 m−3 , and the pressure is 2.75×10 – 10 N/m2 in this space. What is the temperature there?arrow_forward
- If a certain amount of ideal gas occupies a volume V at STP on earth, what would be its volume (in terms of V) on Venus, where the temperature is 1003°C and the pressure is 92 atm?arrow_forwardThe volume V of an ideal gas varies directly with the temperature T and inversely with the pressure P. If a cylinder of 50 liters contains oxygen at a temperature of 200 K and a pressure of 5 atmospheres, what would the gas pressure be if the volume was changed to 30 liters and the temperature raised to 240 K?arrow_forwardCeres is the largest asteriod in the Solar System.But with a mass of q.38 x 102º kg, a radius of 469.73 KM,and a maximum surface temperature of - 38.15°C it doesn't have enough gravity to keep an atmosphere.If the density of Ceres were to remain the same, what would its radius need to be (in kilometers) for itš escape velocity to the rms speed Of Hydrogen gas (H,) ot its maximum svrface temperature?arrow_forward
- The escape velocity of any object from earth is 11.2 km/s. a) express this speed in m/s and km/h. speed, m/s: speed,km/h: b) at what temperature would oxygen molecules (molecular mass is equal to 32 g/mol) have an average velocity, v rms, equal to earths escape velocity 11.2km/s? temperature: Karrow_forwardSuppose P (V, T) gives the pressure P (in N/m? ) of a gas at a volume V (in m³) and temperature T (in ° C). Describe, in a full sentence, what it means if Py (10, 25) = 100arrow_forwardMuch of the gas near the Sun is atomic hydrogen. Its temperature would have to be 1.5×107 K for the average velocity vrms to equal the escape velocity from the Sun. What is that velocity?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College