please help me with question 2.3.2 find the root mean square velocity ?the corre

Question

please help me with question 2.3.2 find the root mean square velocity ?the correct answer are 1.35km/s and 11.2km/s,please show all works.thank you!

A cylinder, volume 10 litres (1 times 10-2m-3), contains 1 kg of an ideal gas, at a pressure of 2.0 Mpa. Calculate the root mean square (r.m.s) velocity of the molecules. Calculate the r.m.s velocity for a 4He atom at 20 degree C. Determine the escape velocity for a projectile at the earth's surface.(rearth = 6.4 times 106m,. mearth = 6.0 times 1024 kg)

Explanation / Answer

M = molar mass of Helium = 4 gm =4*10^-3 kg/mole

Helium is monoatomic molecule ,

If we cosider only translationmotion , then , average energy of Helium = 3RT/2

Kinetic energy =M*Vrms^2

Kinetic energy = 3RT/2

M*Vrms^2 /2= 3*8.32*(273+20)/2

Vrms = [ 7313.28/(4*10^-3)]^0.5 = 1.352*10^3 m/s

Vrms =1.352 km/s

G = gravity constant = 6.67*10^-11

m =6*10^24 kg

R =6.4*10^6

escapse velocity = [2GM/R]^0.5 =[2*6.67*10^-11*m/R]^0.5 = 11.183 km/s

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.