The gas argon very closely approximates an ideal gas. For this problem, let\'s s

Question

The gas argon very closely approximates an ideal gas. For this problem, let's say we have a sample of   6×102 kg    of argon. Some data for argon are given in the table below:

Molar Mass

  4×102 kgmol   

Specific heat at
constant volume

In chemistry you may have seen the formula Q=mcT to compute the heat Q needed to cause a temperature change of  ClicktoEnterTeX in a sample of mass m . The variable c is the specific heat which you would then look up in a table like that given at the start of this problem.

What is the average energy of the argon atoms at   200 K   ?

Assuming no work was done, how much heat energy had to be added to raise the 6×102 kg from   200 K   to   400 K ?

Molar Mass

  4×102 kgmol   

Specific heat at
constant volume

Explanation / Answer

a) First find the rms speed of a mole of argon atoms:
u = sqrt(3RT/M)
u = sqrt[3(8314 J/mol*K)(200 K)/(4.0e-2 kg/mol)]
u = 11167.36 m/s

Now solve for average energy:
E = 1/2(m)(u)^2
E = 0.5(.06 kg)(11167.36.38 m/s)^2
E = 3.7*10^6 J.

b) Q=mcT = 0.06*315(400 - 200)

= 3780 J.

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