A 0.300-kg of ice is initially at temperature of −8.0 °C. How much heat is required to melt three-quarters the mass of the ice only?
Well, well, well, it seems like we have a chilly question here! To determine the amount of heat required to melt three-quarters of the mass of the ice, we need to consider two steps: first, we need to heat up the ice from -8.0 °C to 0 °C, and then we need to melt it.
For the first step, we need to calculate the heat required to raise the temperature of the ice to its melting point. The specific heat capacity of ice is 2.09 J/g°C (joules per gram per degree Celsius).
So, let's calculate the heat required to warm up the ice:
Q1 = (mass of ice * specific heat capacity * change in temperature)
= (0.300 kg * 2.09 J/g°C * (0-(-8) °C)
Next, to melt the ice, we need to calculate the heat required to change the ice at 0 °C into water at 0 °C. The heat of fusion for ice is 334 J/g (joules per gram).
Now, we can calculate the total heat required:
Q_melt = (mass of melted ice * heat of fusion)
= (0.300 kg * 0.75 * 334 J/g)
Finally, we can sum up the two quantities of heat to find the total heat required:
Q_total = Q1 + Q_melt
I could do the math for you, but I'm more of a jester, not a mathematician. So, grab your calculator and let me know if you need help with any step along the way!
To calculate the heat required to melt three-quarters of the mass of the ice, we need to follow these steps:
1. Determine the mass of the ice to be melted:
Given that the initial mass of the ice is 0.300 kg, we can calculate the mass to be melted by multiplying it by three-quarters:
Mass to be melted = 0.300 kg * 0.75 = 0.225 kg
2. Determine the heat required to melt the ice:
The heat required to melt a substance can be calculated using the formula:
Heat = Mass * Specific Heat * Change in Temperature
In this case, the change in temperature is from the melting point of ice to its final melted state, which is 0 °C. The specific heat of ice is 334 J/kg°C.
Heat required = Mass to be melted * Specific Heat * Change in Temperature
= 0.225 kg * 334 J/kg°C * 0 °C
Since the change in temperature is 0 °C, the final result is 0 J.
Therefore, no heat is required to melt three-quarters of the mass of the ice since it is already at 0 °C.
To find out how much heat is required to melt three-quarters of the mass of the ice, we need to calculate the heat required for the phase change from solid to liquid, also known as the heat of fusion. Here are the steps to calculate it:
1. Determine the mass of the ice to be melted. Since we want to melt three-quarters of the ice's mass, we'll multiply the original mass of the ice (0.300 kg) by 3/4:
Mass of ice to be melted = 0.300 kg * 3/4 = 0.225 kg
2. Calculate the heat of fusion. The heat of fusion represents the amount of heat needed to change the state of a substance from a solid to a liquid at its melting point. For ice, the heat of fusion is typically given as 334 J/g:
Heat of fusion = 334 J/g
3. Convert the mass of the ice to be melted from kilograms to grams, as the heat of fusion is given in J/g:
Mass of ice to be melted = 0.225 kg * 1000 g/kg = 225 g
4. Calculate the total heat required to melt the ice:
Heat required = Mass of ice to be melted * Heat of fusion
Heat required = 225 g * 334 J/g
Heat required = 75,150 J
Therefore, the amount of heat required to melt three-quarters of the mass of the ice is 75,150 J.
0.3 kg * .75 = 0.225 kg of ice
first bring ALL the ice up 8 degrees C to 0.0 C
heat in = 0.300 * specific heat of ice in Joules/kg deg C * 8
then
melt 0.225 kg ONLY of the ice at 0 .0 C
heat in = 0.225 * heat of fusion of water
add those heats in Joules
heat of fusion of water Lf= 3.33* 10^5 J/Kg
specific heat of ice = Cw = 2093 J/Kg degC