if 120 g of hot water at 85 degree celsius is poured into an insulated cup containing 200 g of ice at 0 degree celsius. how many grams of liquid will there be when the system reaches thermal equilibrium?
heat to melt x grams ice: x*Hfusion
heat absorbed by warm water: 120*cw*(tf-85)
heat absorbed by melted ice to get to final temperataure: x*cw*(tf-0)
the sum of the heats gained is zero. x is the amount of ice that melted.
xHf+( x)cw*(tf-0)+120(cw)(Tf-85)=0
first, see if all the ices melts, and check Tf.
200*80+200*1*tf+120*1*(tf-85)=0
tf=(120*85-16000 )/200=-29 which is impossible.
So all the ice did not melt, and the final temp is Tf=0
then
x*80+(200-x)Cw(Tf-0)+120*Cw*(Tf-85),but Tf=o if all the ice did not melt, or
80x+0=120*1*85
solve for x, or x=127.5 grams melted, so the water is 120+(200-127.5) g
check my thinking.
To determine the amount of liquid in the system when it reaches thermal equilibrium, we need to calculate the heat gained by the ice and the heat lost by the hot water until they reach the same temperature.
First, we calculate the heat gained by the ice to reach its melting point (0°C), using the equation:
Q = m × Lf
Where:
Q is the heat gained,
m is the mass of ice, and
Lf is the latent heat of fusion for water (which is 334 J/g).
Since the mass of the ice is given as 200 g:
Q_ice = 200 g × 334 J/g
Q_ice = 66800 J
Next, we calculate the heat lost by the hot water to reach its final temperature, using the equation:
Q = m × c × ΔT
Where:
Q is the heat lost,
m is the mass of hot water,
c is the specific heat capacity of water (which is approximately 4.18 J/g·°C),
ΔT is the change in temperature.
The change in temperature is the difference between the final temperature and the initial temperature:
ΔT = 0°C - 85°C
ΔT = -85°C
Since the mass of the hot water is given as 120 g:
Q_water = 120 g × 4.18 J/g·°C × -85°C
Q_water = -427560 J
Now, we can determine the final mass of the system. Since energy is conserved, the heat gained by the ice is equal to the heat lost by the hot water when they reach thermal equilibrium:
Q_ice = Q_water
66800 J = -427560 J
Solving this equation will give a negative mass value, indicating that the final state is entirely liquid. However, since we're interested in the amount of liquid, we'll consider the magnitude of the mass:
Final mass = |66800 J| + |427560 J|
Final mass = 494360 g
Therefore, when the system reaches thermal equilibrium, there will be approximately 494.36 grams of liquid.