How long would it take a 1 200 W heater to melt 1.00 kg of ice at -12.0°C, assuming all the energy from the heater is absorbed by the ice? (Assume the specific heat of the ice is 2 090 J/kg · °C and the latent heat of fusion of water is 3.33 105 J/kg.)
what formula do you use, the fact it asks for time, throws me off
Calculate the number of Joules of heat required (Q), using the mass, specific heat of ice, temperature rise and latent heat of fusion.
Q = M[10 C(ice) + Latent heat]
= 1.00[10*2090 + 3.33*10^5]
= 3.54*10^5 J
Then divide that by the heating rate in Watts (J/s) for the answer in seconds.
calculate the thermal energy required the melt 2kg of ice at 0 c. (lf=3.3x10 jkg-1)
To determine the time it takes for a 1,200 W heater to melt 1.00 kg of ice at -12.0°C, we can use the formula:
Q = mcΔT + mL
Where:
Q is the total heat transferred
m is the mass of the ice
c is the specific heat of ice
ΔT is the change in temperature (final temperature - initial temperature)
L is the latent heat of fusion of water
First, let's calculate the total heat required to raise the temperature of the ice to its melting point (0°C):
Q1 = mcΔT = (1.00 kg)(2,090 J/kg · °C)(0°C - (-12.0°C))
The initial temperature is -12.0°C, and the change in temperature is 0°C - (-12.0°C) = 12.0°C:
Q1 = (1.00 kg)(2,090 J/kg · °C)(12.0°C)
Next, let's calculate the heat required to melt the ice at 0°C:
Q2 = mL = (1.00 kg)(3.33 x 10^5 J/kg)
Now, let's calculate the total heat required to completely melt the ice:
Q_total = Q1 + Q2
Finally, we can determine the time it takes for the heater to transfer this total amount of heat to the ice. As we know that Power = Energy/Time, and we're given the power of the heater (1,200 W), we can rearrange the equation to solve for time:
Time = Energy/Power
Time = Q_total/Power
Substituting the values into the equation, we can calculate the time:
Time = (Q1 + Q2)/(1,200 W)
To calculate the time it would take for a 1,200 W heater to melt 1.00 kg of ice at -12.0°C, we need to consider two processes: heating the ice to its melting point and then melting the ice.
Let's break down the problem step-by-step:
1. Calculate the amount of energy required to heat the ice from -12.0°C to its melting point at 0°C:
- The specific heat capacity of ice is given as 2,090 J/kg · °C.
- The change in temperature is from -12.0°C to 0°C, which is a total of 12.0°C.
- The mass of the ice is given as 1.00 kg.
- Use the formula: Q = mcΔT, where Q is the energy, m is mass, c is specific heat capacity, and ΔT is the change in temperature.
- Plug in the values: Q = (1.00 kg) * (2,090 J/kg · °C) * (12.0°C).
2. Calculate the amount of energy required to melt the ice at its melting point:
- The latent heat of fusion of water is given as 3.33 × 10^5 J/kg.
- The mass of the ice is given as 1.00 kg.
- Use the formula: Q = mL, where Q is the energy, m is mass, and L is the latent heat of fusion.
- Plug in the values: Q = (1.00 kg) * (3.33 × 10^5 J/kg).
3. Calculate the total energy required to both heat and melt the ice:
- Add the energy required for heating and melting together: Total energy = Q_heating + Q_melting.
4. Calculate the time taken by dividing the total energy by the power of the heater:
- The power of the heater is given as 1,200 W.
- Use the formula: time = total energy / power of the heater.
By following these steps and plugging in the given values, you should be able to calculate the time it would take for the heater to melt the ice.