. How much thermal energy must be removed from a 0.25-kg chunk of ice to lower its temperature by 18C ? The specific heat of ice to is 2100 J/kg ⋅K and the heat of fusion for ice is 334×10^3J/kg.
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The calculation involves two steps:
1. First, we need to calculate the amount of heat required to lower the temperature of the ice.
Q1 = m * c * ΔT
where Q1 is the amount of heat, m is the mass of the ice (0.25 kg), c is the specific heat of ice (2100 J/kg ⋅K), and ΔT is the change in temperature (-18C).
Q1 = 0.25 kg * 2100 J/kg ⋅K * (-18C) = -94500 J
Note that the value of ΔT is negative because the temperature is being lowered.
2. Second, we need to calculate the amount of heat required to melt the ice.
Q2 = m * Lf
where Q2 is the amount of heat, m is the mass of the ice (0.25 kg), and Lf is the heat of fusion for ice (334×10^3 J/kg).
Q2 = 0.25 kg * 334×10^3 J/kg = 83,500 J
Note that the value of Lf is positive because the ice is melting.
Therefore, the total amount of thermal energy that must be removed from the ice is:
Q = Q1 + Q2 = -94500 J + 83500 J = -11,000 J
The negative sign indicates that the thermal energy is being removed from the ice. The answer is approximately -11,000 J.
To calculate the amount of thermal energy that needs to be removed from the chunk of ice to lower its temperature by 18°C, we need to consider two factors: the heat required to lower the temperature and the heat required for the phase change from solid to liquid.
First, let's calculate the heat required to lower the temperature of the ice. We can use the formula:
Q = mcΔT
Where:
Q = amount of heat energy
m = mass of the ice (0.25 kg)
c = specific heat capacity of ice (2100 J/kg⋅K)
ΔT = change in temperature (18°C)
Plugging in the values, we get:
Q1 = (0.25 kg)(2100 J/kg⋅K)(18°C)
Next, we need to calculate the heat required for the phase change from solid to liquid. This is done using the formula:
Q2 = mLf
Where:
Q2 = amount of heat energy
m = mass of the ice (0.25 kg)
Lf = heat of fusion for ice (334 × 10^3 J/kg)
Plugging in the values, we get:
Q2 = (0.25 kg)(334 × 10^3 J/kg)
Finally, we can calculate the total thermal energy that needs to be removed by adding Q1 and Q2:
Total thermal energy = Q1 + Q2
Note: Make sure to convert temperature changes to Kelvin by adding 273.15 to Celsius values before plugging them into the formulas.
I hope this helps in calculating the amount of thermal energy required to lower the temperature of the ice!