Answered

A 10.0-g sheet of gold with a temperature of 18.0°C is laid flat on a sheet of iron that weighs 20.0 g and has a temperature of 55.6°C. Given that the specific heats of Au and Fe are 0.129 J g-1 0 c-1 and 0.444 J g-1 0 c-1, respectively, what is the final temperature of the combined metals? Assume that no heat is lost to the surroundings. (Hint: The heat gained by the gold must be equal to the heat lost by the iron.)

Answer :

Answer:

T = 50.83°C

Explanation:

Let the final temperature be T .

heat lost = mass x specific heat x fall in temperature

heat lost by iron = 20 x .444 x ( 55.6 - T )

heat gained  by gold  = 10 x .129 x ( T- 18 )

heat lost = heat gained

20 x .444 x ( 55.6 - T ) = 10 x .129 x ( T- 18 )

493.73 - 8.88 T = 1.29 T - 23.22

10.17 T = 516.95

T = 50.83°C

Lanuel

The final temperature of the combined metals (gold and iron) is 50.83°C.

Given the following data:

  • Initial temperature of gold = 18.0°C
  • Final temperature of iron = 55.6°C
  • Mass of gold = 10.0 g
  • Mass of iron = 20.0 g
  • Specific heat capacity of iron = 0.444 J/g°C.
  • Specific heat capacity of gold = 0.129 J/g°C.

To find the final temperature of the combined metals (gold and iron):

Heat lost by the iron = Heat gained by the gold.

[tex]Q_{lost} = Q_{gained}\\\\mc\theta = mc\theta\\\\20(0.444)(55.6 - T_f) = 10(0.129)(T_f - 18)\\\\8.88(55.6 - T_f) = 1.29(T_f - 18)\\\\493.728 - 8.88T_f = 1.29T_f - 23.22\\\\8.88T_f + 1.29T_f = 493.728 + 23.22\\\\10.17T_f = 516.948\\\\T_f = \frac{516.948}{10.17}[/tex]

Final temperature = 50.83°C

Read more: https://brainly.com/question/188778

Other Questions