After finally gaining entrance to your new square house with its recently instal

Question

After finally gaining entrance to your new square house with its recently installed door, you discover the notes to a long-lost physics experiment. Since physics and the pursuit of knowledge are your only true aspirations, you feel inclined to finish the calculations. The experiment consisted of a 3.50-kg aluminum chamber, filled with 2.75 mol of nitrogen, into which a 0.500-kg hunk of copper was placed. The initial temperature of the aluminum chamber and nitrogen gas was 20.0 degree C while the initial temperature of the hunk of copper was 240.0 degree C. You easily recall that the specific heat for aluminum is c_Al = 9.10 times 10^2 J/kg middot K and the specific heat for copper is c_Cu = 3.90 times 10^2 J/kg middot K. (a) What was the equilibrium temperature for this experiment? Assume that no heat was lost to the surroundings. (b) What was the entropy change for this experiment?

Explanation / Answer

Energy lost by copper = Energy gained by Aluminum chamber + Nitrogen

mcu - Mass of copper=0.5kg

mAl- mass of aluminum=3.5kg

Ccu-Specific heat of copper=3.90 x 102 J/Kg.K

CAl- Specific heat of aluminum=9.10 x 102 J/Kg.K

Teq- Equilibrium temperature

mcu x Ccu x (Teq - (240+273.15)) = mAl x CAl x (Teq - (20+273.15)) + mN x Cv x (Teq - (20+273.15))

Cv =0.743 J/Kg.K

Assuming Cv to be constant

For mN ,

1 mol of nitrogen gas(N2)=28.015g

2.5 mol=70.0375g=70.0375 x 10 -3 kg

Solving the above equation for Teq we get

Teq=278.8K

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