The kinetic energy of any moving particle is KE = ½mv 2 , where m is the particl

Question

The kinetic energy of any moving particle is KE = ½mv2, where m is the particle mass, and v is its velocity. Maxwell and Boltzmann made a conversion for ideal gases, which is, KE = 3kT/2, where K is the Boltzmann Constant (1.38 × 10-23 Joules per Kelvin). Accordingly, the
average velocity of any hydrogen gas (m = 1.674x10-27kg) in the intergalactic medium will be found to be v = (3 kT / m), which (for Hydrogen) reduces to v = (24731.2*T) . Modified from Chapter 18, we have the escape velocity from a mass M, is v2 = GM/r. Manipulating the math,
we find GM/r = 24731.2*T. Further manipulation gives us M = 24731.2*T*r/G.  

With a temperature of 1.0x108 kelvin, Newton's Constant (G) 6.673×10-11 N m2 kg-2, where r = 15 million (1.5 x 107) light years, and 1 light year = 9.461x 1012 km. Determine the minimum total mass ([M] visible and dark matter) in Kg that is binding these gases across the above galactic cluster distance.

   Answer = ____________________________ Kg.

Explanation / Answer

GM/r = 24731.2*T

where G is universol grvitational constant = 6.673×10-12 N m2kg-2

  r is the distance of the body = 15 million light years = 15*106*9.461*1012 km = 141.915*1018km

= 1.4195*1020km

T =abosolute temperature = 1.0*108kelvin

M =(r / G)*2.4731.2*T

=(1.4195*1020/6.673*10-11)*2.4731.2*108

= 0.21273*2.4731.2*1039

M = 0.252609*1039kg

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

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