Steam warming water and glass from 20°C to 45°C

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Homework Statement


What mass of steam initally at 150 degrees celsius is needed to warm 200g of water in a 100g glass container from 20 degrees celsius to 45 degrees celsius?


Homework Equations


I think Q=mc(delta)T


The Attempt at a Solution


using the above equation calculating the energy required to transfer the steam to 100 degrees and then the energy required to convert it to water and then the energy required to raise the water 25 degrees. That is not right though!
 
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That equation alone is not the whole story. What does "convert it to water" do? What values have you used in the equation and how have you used it?