How much heat is needed for converting 7 kg of ice to steam?

[DrMcDreamy]

Homework Statement

7 kg of ice at 0◦C is converted to steam at 100◦C. How much heat is needed? The heat of fusion for water is 79500 cal/kg, its heat of vaporization is 5.4 × 10⁵ cal/kg, and its specific heat is 1000 cal/kg ·◦C. Answer in units of kcal.

Homework Equations

What is the formula that I am supposed to use?

Q=mc$$\Delta$$T ?

 

[Rick88]

You *also* need to use

Q = mL,
where m is the mass and L is the heat of fusion/vaporisation.R.

 

[tweety1234]

you go from solid to liquid to gas, so you have to calculate the heat for each stage than add up the total of each stage. I think, also, for the vaporization you would use Q =ml where L = latent heat of vaporization.. and Q=ml again for latent heat of fusion/melting

I think that's how you do it...

 

[Rick88]

You should end up with 3 separate values for Q which you will have to add up.

 

[DrMcDreamy]

So:

Q=mc$$\Delta$$T
Q=(7kg)(1000 cal/kg C)(100 C)
Q= 700,000 cal

heat of fusion:
Q=mL
Q=(7kg)(79500 cal/kg)
Q= 556,500 cal

heat of vaporization:
Q=mL
Q=(7kg)(5.4x10⁵ cal/kg)
Q=3,780,000 cal

$$\sum$$Q= 700,000 + 556,500 + 3,780,000

$$\sum$$Q=5,036,500 cal = 5036.5kcal

Is that how?!

 

[Rick88]

Indeed :)

 

[DrMcDreamy]

Thank you!