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A blacksmith forging a 945.0-g knife blade drops the steel blade, initially at 670.0°C, into a...

A blacksmith forging a 945.0-g knife blade drops the steel blade, initially at 670.0°C, into a water trough containing 42.0 kg of water at 21.0°C. Assuming none of the water boils away or is lost from the trough and no energy is lost to the surrounding air, what is the final temperature of the water–knife blade system? Assume  csteel = 450 J/(kg · °C).

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Answer #1

Total energy is conserved

Energy given by the hot steel = Energy gained by water.

Heat energy, H = m*c*dT

​Temperature of steel = 670 + 273 = 943 K

Temperature of water = 21 + 273 = 294 K

​Where m is the mass, c is the specific heat and dT is the change in temperature.

Take the final temperature of the system as T

Msteel*Csteel * [943 - T] = Mwater * Cwater * [T - 294]

0.945 * 450 * [943 - T] = 42 * 4181 [T - 294]

401010.75 - 425.25 T = 175602 T - 51626988

176027.25 T = .52027998.75

T = 295.56 K

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