A sheet of gold weighing 12.0 g and a temp of 28.0 C is placed on a sheet of copper weighing 34.0 g and a temp of 562 C. What is the final temp of the combined metals? Specific heats of gold and copper are 0.129 J/gC and 0.385 J/gC. No heat is lost to the surrounding. The heat gained by the gold must be equal to the heat lost by the copper. I can work the problem till I get to this: tf - 28.0 8.44 tf + 474. Now I‘m lost. Ant advice or help please? Thank you!!
So first you would list the variables that you do know so there's no confusion. Gold: m 12.0 g c 0.129 J/g°C Tf ? Ti 28.0 °C Copper: m 34.0 g c 0.385 J/g°C Tf ? Ti 56.2 °C Then you plug them into the equation: mc(Tf – Ti) mc (Tf – Ti) (12.0)(0.129)(Tf – 28) (34)(0.385)(Tf – 56.2) 1.548(Tf – 28) 13.09(Tf – 56.2) 1.548 Tf – 43.344 13.09 Tf – 735.658 1.548 Tf 13.09 Tf – 692.314 -11.542 Tf -692.314 Tf 59.98 60 °C
Q(gained by gold) Q(lost by copper) (12.0 g)(0.129 J/g-°C)(Tf - 28.0°C) (34.0 g)(0.385 J/g-°C)(56.2°C - Tf) 1.548*Tf - 43.344 J 735.658 J - 13.09*Tf (1.548 + 13.09)Tf 735.658 - 43.344 Tf 47.3°C
So first you would list the variables that you do know so there's no confusion. Gold: m 12.0 g c 0.129 J/g°C Tf ? Ti 28.0 °C Copper: m 34.0 g c 0.385 J/g°C Tf ? Ti 56.2 °C Then you plug them into the equation: mc(Tf – Ti) mc (Tf – Ti) (12.0)(0.129)(Tf – 28) (34)(0.385)(Tf – 56.2) 1.548(Tf – 28) 13.09(Tf – 56.2) 1.548 Tf – 43.344 13.09 Tf – 735.658 1.548 Tf 13.09 Tf – 692.314 -11.542 Tf -692.314 Tf 59.98 60 °C
Q(gained by gold) Q(lost by copper) (12.0 g)(0.129 J/g-°C)(Tf - 28.0°C) (34.0 g)(0.385 J/g-°C)(56.2°C - Tf) 1.548*Tf - 43.344 J 735.658 J - 13.09*Tf (1.548 + 13.09)Tf 735.658 - 43.344 Tf 47.3°C
I'll start from scratch. Heat gained by Au (mass Au)(sp.ht. Au)(Tf - Ti) Heat lost by Cu (mass Cu)(sp.ht. Cu)(Ti - Tf) You're right, these are equal to each other. (mass Au)(sp.ht. Au)(Tf - Ti) (mass Cu)(sp.ht. Cu)(Ti - Tf) (12.0 g)(0.129 J/g C)(Tf - 28.0 C) (34.0 g)(0.385 J/g C)(56.2 - Tf) 1.55 (Tf - 28.0) 13.1 (56.2 - Tf) 1.55 Tf - 43.4 736 - 13.1 Tf 14.7 Tf 693 Tf 47.1 C
I'll start from scratch. Heat gained by Au (mass Au)(sp.ht. Au)(Tf - Ti) Heat lost by Cu (mass Cu)(sp.ht. Cu)(Ti - Tf) You're right, these are equal to each other. (mass Au)(sp.ht. Au)(Tf - Ti) (mass Cu)(sp.ht. Cu)(Ti - Tf) (12.0 g)(0.129 J/g C)(Tf - 28.0 C) (34.0 g)(0.385 J/g C)(56.2 - Tf) 1.55 (Tf - 28.0) 13.1 (56.2 - Tf) 1.55 Tf - 43.4 736 - 13.1 Tf 14.7 Tf 693 Tf 47.1 C
