Is this question on heat right?

[Aceix]

Homework Statement

A 250g calorimeter made of a certain metal contains 200g of water at 28'C. When 500g mass of the same metal and at a temperature of 117'C is dropped gently onto the water, an amount of the water boils off whiles the remaining wager rises to 45'C. Calculate the mass of water that boiled off at the boiling point of 100'C.

Specific heat capacity of metal=420J/kg K
Specific latent heat of vaporisation of water=2.456x10^6J/kg
Specific heat capacity of water=4200J/kg K

Homework Equations

The Attempt at a Solution

I think the question is not making any sense because how can the water boil an still be at 45'C(1.0atm) since boiling occurs at a constant temperature(100'C)?

 

[Mark44]

Homework Statement

A 250g calorimeter made of a certain metal contains 200g of water at 28'C. When 500g mass of the same metal and at a temperature of 117'C is dropped gently onto the water, an amount of the water boils off whiles the remaining wager rises to 45'C. Calculate the mass of water that boiled off at the boiling point of 100'C.

Specific heat capacity of metal=420J/kg K
Specific latent heat of vaporisation of water=2.456x10^6J/kg
Specific heat capacity of water=4200J/kg K

Homework Equations

The Attempt at a Solution

I think the question is not making any sense because how can the water boil an still be at 45'C(1.0atm) since boiling occurs at a constant temperature(100'C)?

The water closest to the heated mass can get hot enough to boil without the entire body of water getting to the boiling point.

Also, the boiling point of water is not a constant - the BP changes with ambient air pressure. Lower air pressure is tied to a lower boiling point.

 

[Aceix]

Then I can say
Heat lost from hot metal at 177'C goes to increase the temperature of m mass of water to 100'C and turns it to vapour, some increases the temp of the calorimeter and the remaining increases the temp of (200-m)g of the water to 45'C?

Aceix.

 

[haruspex]

Then I can say
Heat lost from hot metal at 177'C goes to increase the temperature of m mass of water to 100'C and turns it to vapour, some increases the temp of the calorimeter and the remaining increases the temp of (200-m)g of the water to 45'C?

Aceix.

Yes.