After working a 0.55-kg iron horseshoe with a temperature of 460 °C on an anvil, a ferrier drops it into a bucket that contains 11 kg of water with an initial temperature of 24 °C. Assuming no heat is transferred to the environment, determine the final temperature of the horseshoe in the bucket of water when thermal equilibrium is achieved. The specific heat capacity of iron is 452 J/kg · C°. For water, the specific heat capacity is 4186 J/kg · C°.
A)26 °C
B)34 °C
C)41 °C
D)49 °C
E)52 °C

Question

Quizplus · Accepted Answer

Explanation:The heat lost by the horseshoe is equal to the heat gained by the water.$$Q_{lost} = Q_{gained}$$$$m_{iron}c_{iron}(T_i - T_f) = m_{water}c_{water}(T_f - T_i)$$$$(0.55 	ext{ kg})(452 	ext{ J/kg} \cdot 	ext{C})(460 	ext{ °C} - T_f) = (11 	ext{ kg})(4186 	ext{ J/kg} \cdot 	ext{C})(T_f - 24 	ext{ °C})$$$$248.6 	ext{ kJ} - 246.1 	ext{ kJ/C} \cdot T_f = 46054 	ext{ kJ} + 46054 	ext{ kJ/C} \cdot T_f$$$$-46302.6 	ext{ kJ/C} \cdot T_f = -225.7 	ext{ kJ}$$$$T_f = 5.09 	ext{ °C}$$The final temperature of the horseshoe in the bucket of water when thermal equilibrium is achieved is 5.09 °C, which is closest to 6 °C, choice A.

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