What Is the Final Temperature When Ice Melts in Water?

AI Thread Summary
The discussion revolves around calculating the final temperature when 0.50 kg of ice at 0°C is added to 1 kg of water at 20°C in an insulated cup. The key equations involve the heat gained by the ice and the heat lost by the water, leading to the equation Q_gain(ice) = Q_lost(water). The calculations show that the total energy required to melt the ice and the energy available from the water are critical to determining the final temperature. The attempt at a solution indicates that the final temperature is calculated to be approximately -13.3°C, which suggests a misunderstanding since temperatures cannot be negative in this context. The discussion highlights the importance of considering energy conservation and phase changes in thermal equilibrium problems.
cugirl
Messages
17
Reaction score
0

Homework Statement



An insulated cup contains 1kg of water initially at 20 C. 0.50 kg of ice, initially at
0 C is added to the cup of water. The water and ice are allowed to come to thermal equilibrium. The specific heat of ice is 2000 J/kg oC, the specific heat of water 4186 J/kg oC, the latent heat of fusion of water is 33.5x104J/kg. What is the final temperature of the water?

(A) 0 C
(B) 1.2 C
(C) 4.6 C
(D) 9.2 C
(E) 15.2 C



Homework Equations


Q_gain(ice) = Q_lost(water)
mc(Ti-Tf) = mLf + mc(Tf-0)


The Attempt at a Solution


Q_gain(ice) = Q_lost(water)
mc(Ti-Tf) = mLf + mc(Tf-0)
(1.0)(4186)(20 - Tf) = (.5)( 33.5x104 ) + (.5)(4186)(Tf)
83,720 – 4186Tf = 167,500 + 2093 Tf
-83780= 6279 Tf
-13.3 = Tf
 
Physics news on Phys.org
Correct method
But what is the total energy needed to melt the ice?
How much energy can you get from the initial water before it cools to 0c?
 
Last edited:
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanged mass'

Thread 'A cylinder connected to a hanged mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Thermodynamics - Latent Heat Problem (finding mass)
Replies
7
Views
2K
Question about thermal physics -- Ice cubes melting in water
Replies
8
Views
3K
Calorimetry - finding the final temperature of a system of ice and water
Replies
7
Views
2K
Ice in water question - what is final temperature?
Replies
11
Views
5K
I try to solve a thermodynamics problem on heat transfer
Replies
3
Views
2K
Thermodynamics adding ice to water problem with latent heat
Replies
1
Views
3K
How many kg of ice must be dropped to make Tf= 22.7C?
Replies
9
Views
2K
Mixing water and ice
Replies
12
Views
857
Final temperature after pouring soda into glass with ice....
Replies
5
Views
6K
Heat Capacity and Latent Heat question
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top