Steam = 100C -- how much steam got injected into the water to heat it up?

[Yeahaight]

Homework Statement

To heat 4 kg of water from 10 C to 90 C, 100 C water vapor was injected. How much steam was injected?
Given values:
m1 = 4kg
t1 = 10 C
t2 = 90 C
t = 100 C
c water = 4,2*10^3 J/kg*k
r = 22,6*10^5 J/K

Relevant Equations

Q = r*m
Q = c*m(t2-t1)

I guess, firstly I have to calculate the heat that is needed.
Q=c*m(t2-t1)
I'm not sure what to do further from here.

 

[BvU]

I'm not sure what to do further from here

You set up a heat balance: heat given off = heat taken up

 

[Yeahaight]

You set up a heat balance: heat given off = heat taken up

Well, heat taken up would be - Q = c water*m1*(t2-t1)?
I'm not sure about heat given off, though.

 

[Chestermiller]

What is the definition of r?

 

[Lnewqban]

...
I'm not sure about heat given off, though.

In ideal conditions, steam cools down inside the mass of water until becoming water itself.
This is how it works in real life:
https://www.spiraxsarco.com/learn-a...er/heating-vats-and-tanks-by-steam-injections

 

[BvU]

I'm not sure about heat given off, though

So you want to find out how much heat is given off by starting out with x kilograms of water vapour at 100 $^\circ$C and ending up with ... ?

How do you combine your relevant equations to describe this process ?

 

[DrClaude]

I have deleted some posts. Please do not provide a full solution, but instead help the OP do the work.