Final answer:
It takes approximately 199 minutes, or 3 hours and 19 minutes, for the ice to start melting.
Step-by-step explanation:
The question states that an open container holds ice at a temperature of -11.1°C, with a mass of 0.505 kg. To find out how much time passes before the ice starts to melt, we need to calculate the amount of heat required to raise the temperature of the ice from -11.1°C to 0°C and then the amount of heat required to melt the ice.
First, we calculate the heat required to raise the temperature of the ice using the specific heat capacity of ice. Q1 = mcΔT, where Q1 is the heat required, m is the mass of the ice, c is the specific heat capacity of ice (2100 J/kg⋅K), and ΔT is the change in temperature (-11.1°C to 0°C).
Q1 = (0.505 kg)(2100 J/kg⋅K)(11.1°C) = approximately 11,226 J.
Next, we calculate the heat required to melt the ice using the latent heat of fusion. Q2 = mLf, where Q2 is the heat required, m is the mass of the ice, and Lf is the latent heat of fusion for ice (334×10³ J/kg). Q2 = (0.505 kg)(334×10³ J/kg) = approximately 168.67×10³ J.
Finally, we determine the total heat required to raise the temperature of the ice and melt it. Q total = Q1 + Q2 = 11226 J + 168.67×10³ J = approximately 179,100 J.
Since heat is supplied at a constant rate of 900 J/minute, we can determine the time it takes to melt the ice by dividing the total heat required by the heat supplied per minute. t = Q total / heat supplied per minute = 179100 J / 900 J/minute = approximately 199 minutes.
Therefore, it takes approximately 199 minutes, or 3 hours and 19 minutes, for the ice to start melting.