Question

Please show work. Thank you!!

Question 3:

1. ) Air contains approximately 80% N₂ and 20% O₂.
   1. At STP, what is the rms speed of O₂ molecules in air?
   2. At STP, what is the average KE of an O₂ molecule?
   3. At STP, what is the rms speed of N₂ molecules?
   4. If we don’t distinguish between N₂ and O₂, what would be the average rms speed?

1. Actual question:) Now consider the same situation as in problem (3) but the 50 cm long rod is half aluminum and half copper. The aluminum end is in boiling water.

1. What would be the steady temperature of the Al-Cu junction?
2. How much ice will the rod melt in 20 minutes.

Answer 1

Q.3-

a) at stp, T=273.15 k

also we know V_rms= (3RT/M)^0.5

V _{rms (o)}=(3*8.314*273.15/0.032)^0.5

where,R=8.314 jmol^-1 K^-1  

M=32g/mol =0.032kg/mol

hence, V_rms(o)= 461.3m/s

b) avg K.E_o =1/2*M*V_rms(o)²

this gives , K.E_o=0.5*0.032*(461.3)²

=3404.763 J

c) similarly for nitrogen, M =28g/mol =0.028kg/mol

hence V_rms(n) = 493.27 m/s

d) avg molecular weight of air = mol fraction of Nitrogen*mol wt of nitrogen + mol fraction of oxygen*mol wt of oxygen

= 0.8*28 +0.2*32 = 28.8g/mol

M_air =0.0288kg/mol

hence V_{rms (air)} =(3*8.314*273.15/0.0288)^0.5

=486.37 m/s

(Actual question)- datas are not available for this question like , thermal conductivity of aluminium and copper ,also the temperature of copper end .

Theoritically, at steady state , the heat from boiling water (at 373.15 K ,as it is theboiling temperature of water) to aluminium=the heat from aluminium to copper =the heat from copper to ice (if copper is at ice temperature)

we know that, heat= k*dT/dx (fourier's law)

find out temperature at junction from this equation ,and this heat is used to melt the ice !