A144.7 g piece of copper (specific heat 0.38 j/g･°c) is heated and then placed into 400.0 g of water initially at 20.7°c. the water increases in temperature to 22.2°c. what is the initial temperature of the copper? (the specific heat of water is 4.18 j/g･°c).

The initial temperature of the copper is 67.81 °C

Explanation:

Step 1: Data given

Mass of copper = 144.7 grams

Mass of water = 400.0 grams

specific heat of copper = 0.38 J/g°C

Specific heat of water = 4.18 J/g°C

Initial temperature of water = 20.7 °C

Initial temperature of copper = TO BE DETERMINED

Final temperature of water and copper = 22.2 °C

Step 2: Calculate initial temperature of copper

Qgained = -Qlost

Q(water) = -Q(copper)

Q = m*c*ΔT

m(water) * c(water) * ΔT(water) = - m(copper) * c(copper) * ΔT(copper)

400 * 4.18 * (22.2 - 20.7) = - 144.7 * 0.38 * ΔT(copper)

2508 = -54.986 ΔT(copper)

ΔT(copper) = 2508/-54.986

ΔT(copper)= -45.61

ΔT(copper) =-45.61 =  22.2° - T1

T1 = 22.2°C + 45.61 = 67.81 °C

The initial temperature of the copper is 67.81 °C