How much steam to raise vessel temperature from 0 to 28 C?

[JustinLiang]

Homework Statement

A vessel whose walls are thermally insulated contains 2.40kg of water and 0.450kg of ice, all at a temperature of 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.

Homework Equations

Q=mc∆t
Q=mL
Water heat of fusion - 334000
Water heat of vaporization - 2256000
specific heat of water - 4190

The Attempt at a Solution

I am pretty sure my logic is right but my answer does not match with the book answer. I think the book may be wrong... The answer in the book is 190g.

What I did was:
Q(melting ice) + Q(water + melted ice from 0 C to 28 C) = Q(vaporization)
(0.45kg)(334000) + (0.45kg+2.4kg)(4190)(28K) = m(2256000)

I solved for m and I get 214.8g.

Am I doing anything wrong? If so what?

Thanks.

 

[PeterO]

Homework Statement

A vessel whose walls are thermally insulated contains 2.40kg of water and 0.450kg of ice, all at a temperature of 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.

Homework Equations

Q=mc∆t
Q=mL
Water heat of fusion - 334000
Water heat of vaporization - 2256000
specific heat of water - 4190

The Attempt at a Solution

I am pretty sure my logic is right but my answer does not match with the book answer. I think the book may be wrong... The answer in the book is 190g.

What I did was:
Q(melting ice) + Q(water + melted ice from 0 C to 28 C) = Q(vaporization)
(0.45kg)(334000) + (0.45kg+2.4kg)(4190)(28K) = m(2256000)

I solved for m and I get 214.8g.

Am I doing anything wrong? If so what?

Thanks.

Don't forget that once the steam has condensed from steam at 100 C to water at 100 C, then that water at 100 C has to cool to 28 C.

I don't see anything changing temperature by 72 C in your calculation.