A 10 kg block of ice has a temperature of -13°C. The pressure is one atmosphere. The block absorbs 4.10 106 J of heat. What is the final temperature of the liquid water?
I multiplied 10kg by -13 and divided by the heat absored by the block 4.10*10^6 but i can get the right answer
You need to do the problem in three parts: (1) The heating of the ice to 0 C, (2) the melting of the ice, and (3) the heating of the liquid water. First caclulate the amount of heat needed to heat the 10 kg to 0 C, and then the amount needed to heat the ice at 0 C. The remainder of the 4.10*10^6 J (after subtracting the previous two amount) is available to heat the liquid water.
To solve this problem, you need to take into account the specific heat capacity of ice and water. The specific heat capacity of ice is 2.09 J/g°C, and the specific heat capacity of water is 4.18 J/g°C.
First, convert the mass of the block of ice from kg to grams.
10 kg = 10,000 g
Next, calculate the energy required to raise the temperature of the ice from -13°C to 0°C (melting point of ice).
Energy = mass (g) * specific heat capacity (J/g°C) * change in temperature (°C)
Energy = 10,000 g * 2.09 J/g°C * 13°C = 270,700 J
Next, calculate the energy required to melt the ice.
Energy = mass (g) * heat of fusion (J/g)
Energy = 10,000 g * 334 J/g = 3,340,000 J
The total energy absorbed by the block of ice is the sum of the energy required to raise the temperature and the energy required to melt the ice.
Total energy absorbed = 270,700 J + 3,340,000 J = 3,610,700 J
Now, calculate the energy remaining to raise the temperature of the water.
Energy remaining = total energy absorbed - heat absorbed (4.10 * 10^6 J)
Energy remaining = 3,610,700 J - 4.10 * 10^6 J = -489,300 J
Since the energy remaining is negative, it means that the water does not need any additional heat to reach its final temperature. Therefore, the final temperature of the water is 0°C
To find the final temperature of the liquid water, you need to use the equation for heat transfer:
Q = mcΔT
Where:
Q = heat absorbed or released (in joules)
m = mass of the substance (in kg)
c = specific heat capacity of the substance (in J/kg°C)
ΔT = change in temperature (in °C)
First, you need to determine the heat absorbed by the block of ice. You stated that the block absorbs 4.10 * 10^6 J of heat, so Q = 4.10 * 10^6 J.
Next, you need to determine the specific heat capacity of ice. The specific heat capacity of ice is 2.09 J/g°C or 2090 J/kg°C. Note that you should convert the units to match the units of your other values, which are in kilograms.
Now, substitute the known values into the equation and solve for ΔT:
4.10 * 10^6 J = (10 kg) * (2090 J/kg°C) * ΔT
Simplifying:
ΔT = (4.10 * 10^6 J) / (10 kg * 2090 J/kg°C)
ΔT ≈ 196.65°C
Finally, you need to find the final temperature by subtracting the initial temperature from ΔT:
Final temperature = (-13°C) + (ΔT ≈ 196.65°C)
Final temperature ≈ 183.65°C
So, the final temperature of the liquid water is approximately 183.65°C.