Physics problem, ten points for most thorough answer.?

Question

An insulated beaker with negligible mass contains a mass of 0.280 kg of water at a temperature of 76.2 degrees C.

How much ice at a temperature of - 23.6 degrees C must be dropped in the water so that the final temperature of the system will be 36.9 degrees C?
Take the specific heat for water to be 4190 J/(kg*K), the specific heat for ice to be 2100 J/(kg*K), and the heat of fusion for water to be 334 kJ/kg.

Answer 1

I donno ;=)

May be start with a heat balance equation like

Qfinal=Qwater-start - Qice-start – Qlatent

In other words the final heat of the system is equal to the original amount of heat minus the heat required to bring ice to the melting point and minus again the amount of heat needed to melt the ice

Or
Qfinal=(Specific-heat of water) (temp in K)(mass-final)

mass-final= mass of water + mass of ice= m1 + m2

Note -273.16 °C =0 degrees on Celsius scale = 273.16 °K (273 I hope is good enough for you?)

Qwater-start =( 4190 J/(kg*K) (t-start K degrees )(m1)( 4190 J/(kg*K)=A(m1) A= 4190 (76.2 + 273)

Qice-start= 2100 J/(kg*K)( - 23.6+273)(m2)= B(m2)


Qlatent= 334 kJ/kg(m2) =C(m2)

We have

D(m1+m2)=A(m1)+B(m2)+C(m2) you know that m1=.280kg then you figure out m2?
And
A= 4190 (76.2 + 273)
B=2100 (- 23.6+273)
C=334,000

Actually Specific heat of ice = 2060 J/(kg*K) not 2100 J/(kg*K)
And Specific heat of water =4,183 J/(kg*K)

Answer 2

27

Answer 3

Heat required to bring ice to 0degree= X*2100* 23.6=49560X
Heat required for Ice to melt = 334000X
Heat required for this water @ zero degree (from melted Ice) to reach 36.9=36.9 *4190*X=154611X
HEAT lost by water= 0.28*4190*(76.2-36.9)=46106

Energy Balance

Heat Lost =Heat required.
46106.76=538171X

===> x= 0.0856 kG of ice will do it :)

Hey previous author forgot the heat required for the ice to bring @ zero degree celcius before it starts melting

I love Physics !!!\

Answer 4

Are you actually interested in how you need to proceed to understand and work the problem yourself? One would hope so...

You need to make the argument that whatever heat energy the hot water gives up is equal to the heat energy gained by the ice as it melts and warms up. Set this up as an equation and solve it for the mass of ice needed.

The hot water loses an amount of energy equal to its mass times its specific heat times its temperature change.

The ice gains an amount of energy equal to the sum of two things: the energy needed to melt it (its mass times its heat of fusion) and the energy need to raise the melted ice (starting at 0 C) to the final temperature.

This should be enough for you to put in the numbers and solve the relationship.

Answer 5

Do your own homework!!

Answer 6

Sorry, this is your HW.