Department of Materials and Metallurgical Engineering Bangladesh University of Engineering and Technology, Dhaka MME6701 Thermodynamics and Kinetics of Materials Solutions to Problems of Class Test 2 3. The activity coefficient of zinc in liquid brass has been expressed for the temperature range 1000 to 1500 K by the equation RT ln Zn = –4600(XCu)2 where R in J/mol-K and T in K. Calculate the activity of copper of a solution containing 60 atom per cent copper at 1500 K. Solution ln = −4600 ln = − = − 4600 4600 8.314 . 1773 = −0.312 Now, . ln = − ln . . ln = − . . (−0.312 . 2 = − . . = +0.624 . . = −0.624 . = −0.624 ln 2 = −0.05 . = = 0.95 Then, the activity of copper = . = 0.95 (0.60) = 0.57 ) 4. A steel solution contains 0.6 % C, 1.0 % Mn, 0.3 % Si, and 0.8 % Cr (by weight). Calculate the activity of carbon at 1000 °C, when the standard state of carbon is 1.0 % carbon. At 1000 °C, CC = 8.7, CMn = –4.3, eCSi= 11.2, eCCr= –12. The atomic weights of C, Mn, Si and Cr are 12, 55, 28 and 52, respectively. What will be the activity of carbon if the standard state of carbon is graphite. Use C0 = 7.9. Solution The Henrian activity of carbon ℎ = . % = . log ℎ = log . . + log = . + log % + % % + log + + log % + % % + log + log % % Now since 0.2425 = 0.2425 = = 0.2425 0.2425 (8.7) = 0.18 12 = = 0.2425 (−4.3) = −0.02 55 Then log ℎ = % + % + % + % = (0.18)(0.6) + (−0.02)(1.0) + (11.2)(0.3) + (−12)(0.8) + log(0.6) = −6.37 ℎ = 4.23 10 Now since ℎ = = ℎ = (4.23 10 )(7.9) = 3.34 10

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