What is the final temperature of the water when ice is added to it?

[missileblitz]

Question #1

Homework Statement

How much heat will be lost when 120 g of steam at 100°C is condensed to water at 80°C?

Homework Equations

Q = mc∆t
Q = m LV

The Attempt at a Solution

Q = mc∆t
Q = 0.12 x 4186 x (80 – 100)
Q = 10046.4 J
Q = m LV
Q = 0.12 x (- 2.3 x 106)
Q = 276000 J
= 10046.4 + 276000 = 286046.4
= -2.9 x 105 J

Is the latent heat of condensation negative to that of vaporization?

Question #2

Homework Statement

If 20 g of ice at 0° is added to 180 g of water at 22°C, what will the final temperature of the water be?

Homework Equations

Q = mc∆t

The Attempt at a Solution

mc∆t = mc∆t
0.02 x 2050 (0-T) = 0.18 x 4186 (T-22)
-41T = 753.48T - 16576.56
-794.48T = -16576.56
-794.48T/-794.48 = -16576.56/-794.48
T = 20.86

For this question, is the latent heat of fusion needed?

 

[Mapes]

Yes, it has the opposite sign, as energy is required for vaporization but released by condensation. You calculations look good.

 

[missileblitz]

Yes, it has the opposite sign, as energy is required for vaporization but released by condensation. You calculations look good.

Thanks for the reply! I'd like someone to confirm the second question too. Thanks in advance.

 

[missileblitz]

:O no one?

 

[rl.bhat]

:O no one?

Heat lost by water = m_wc(22 - t)

Heat gained by the ice = m_iL + m_ic(t-0) where L is the latent heat of fusion of ice.

Now solve for t.

 

[missileblitz]

Heat lost by water = m_wc(22 - t)

Heat gained by the ice = m_iL + m_ic(t-0) where L is the latent heat of fusion of ice.

Now solve for t.

Many thanks for your reply!