Heat required to heat water and ice

[Elias Waranoi]

Is the answer in my physics book wrong or did I miss something?

Homework Statement

A vessel whose walls are thermally insulated contains 2.40 kg of water and 0.450 kg of ice, all at 0.0°C. The outlet of a tube leading from a boiler in which water is boiling at atmospheric pressure is inserted into the water. How many grams of steam must condense inside the vessel (also at atmospheric pressure) to raise the temperature of the system to 28.0°C? You can ignore the heat transferred to the container.

m_w = 2.4 kg
m_i = 0.45 kg
ΔT = 28 C°
c = 4190
L_f 334 * 10^3 J/kg
L_v 2256 * 10^3 J/kg

Homework Equations

Q = mcΔT
Q = ±mL

The Attempt at a Solution

Heat required to melt ice and warm water to 28 C°:
Q_req = m_iL_f + (m_i + m_w)cΔT

Condensing steam of amount Q_req = -m_sL_v
m_s = -(m_iL_f + (m_i + m_w)cΔT)/L_v
m_s = -215 grams

My physics book tells me the answer is 190 grams, which I get if I don't account for m_i in (m_i + m_w)cΔT. This seems wrong to me but I wanted to ask and make sure, every other time I've claimed that I found an error in my physics book I have been incorrect.

 

[gneill]

When the steam condenses, is it at the final temperature?

 

[Elias Waranoi]

Oops, thank you I got it right now.