Please explain the steps of this problem and show the formula(s) used:

Question

A 5.0 g piece of metal is heated to 100ºC, then placed in a beaker containing 20.0 g of water at 10ºC. The temperature of the water rises to 15ºC. Assuming that heat lost by the metal = heat gained by the water. Calculate the specific heat of the metal.

Answer 1

One more time...

The heat gained or lost = q = mC∆T

q = heat; m = mass; C = specific heat; ∆T = change in temperature

Heat lost by metal = heat gained by water

Step 1 - heat lost by metal

mass of metal = 5.0 g; C = ?; ∆T = 85º because the temperature went from 100º to 15º

q = mC∆T = (5.0 g)(C)(85)

Step 2 - heat gained by water

mass of water = 20.0 g; C = 4.184 J/gº; ∆T = 5º because the temperature went from 10º to 15º

q = mC∆T = (20.0 g)(4.184 J/gº)(5º)

Step 3 - set the 2 equations equal to each other and solve for the unknown, C

q = mC∆T = (5.0 g)(C)(85) = q = mC∆T = (20.0 g)(4.184 J/gº)(5º)

425C = 418.4

C = 0.984 J/gº