A 400-g block of iron at 400°C is dropped into a calorimeter (of negligible heat capacity)containing 60 g of water at 30°C.How much steam is produced? The latent heat of vaporization of water is 22.6 × 10⁵ J/kg and its specific heat capacity is 4186 J/kg ∙ K.The average specific heat of iron over this temperature range is 560 J/kg ∙ K. A)22 g B)33 g C)42 g D)54 g E)59 g

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Quizplus · Accepted Answer

The heat lost by the iron block is equal to the heat gained by the water and the steam produced. The heat lost by the iron block is:Q = mcΔt = (0.4 kg)(560 J/kg ∙ K)(400°C - 30°C) = 90.2 kJThe heat gained by the water is:Q = mcΔt = (0.06 kg)(4186 J/kg ∙ K)(100°C - 30°C) = 12.5 kJThe heat gained by the steam produced is:Q = mL = m(22.6 × 10⁵ J/kg)The total heat gained by the water and the steam produced is:Q = 12.5 kJ + m(22.6 × 10⁵ J/kg)Setting this equal to the heat lost by the iron block, we get:90.2 kJ = 12.5 kJ + m(22.6 × 10⁵ J/kg)Solving for m, we get:m = (90.2 kJ - 12.5 kJ) / (22.6 × 10⁵ J/kg) = 0.0035 kg = 3.5 gTherefore, the amount of steam produced is 3.5 g.

A 400-G Block of Iron at 400°C Is Dropped into a Calorimeter