An open container holds ice of mass 0.540 kg at a temperature of -18.7 c The mass of the container can be ignored. Heat is supplied to the container at the constant rate of 790 J/minute.

The specific heat of ice to is 2100 J/kg . K and the heat of fusion for ice is 334 * 10^3 J/kg.

A) How much time passes before the ice starts to melt?

B) From the time when the heating begins, how much time does it take before the temperature begins to rise above 0 C?

Q1 = cmΔ= 2100•0.54•18.7 = 2.12•10^4 J.

Q2 = r•m = 334•103•0.54= 1.8•10^5 J.

Q1/q = 2.12•10^4/790 = 26.8 min – 0.45 h.
(Q1+Q2)/q = (2.12•10^4 + 1.8•10^5)/790 = 255.1 min = 4.25 h.

A) Well, it seems like the ice is pretty chill right now, but let me do some calculations to thaw out the answer for you. The total energy required to melt the ice can be calculated using the formula: Q = m * Hf, where Q is the heat required, m is the mass of the ice, and Hf is the heat of fusion for ice. Plugging in the values, we get Q = 0.540 kg * 334 * 10^3 J/kg. Now we need to find out how long it will take to supply this amount of heat. Since heat is supplied at a constant rate of 790 J/minute, we can use the formula: Q = P * t, where Q is the heat required, P is the power, and t is the time. Rearranging the formula to solve for time, we get t = Q / P. Plugging in the values, we have t = (0.540 kg * 334 * 10^3 J/kg) / 790 J/minute. Time to put on my thinking cap! After crunching some numbers, I found out that it will take approximately 226.27 minutes before the ice starts to melt. That's quite a chilling waiting period, don't you think?

B) Ah, let's see when things start to heat up, shall we? In order to find out how long it takes for the temperature to rise above 0°C, we need to calculate the additional heat required to warm up the ice to 0°C. The formula to find the heat required is: Q = m * c * ΔT, where Q is the heat required, m is the mass of the ice, c is the specific heat capacity of ice, and ΔT is the change in temperature. Plugging in the values, we have Q = 0.540 kg * 2100 J/kg·K * (0°C - (-18.7°C)). Now, using the same formula as before, we can find the time it takes to supply this additional heat. So, t = Q / P, where t is the time, Q is the heat required, and P is the power. Substituting the values, we have t = (0.540 kg * 2100 J/kg·K * (0°C - (-18.7°C))) / 790 J/minute. After some comedic calculations, I can confidently tell you that it will take approximately 45.24 minutes for the temperature to rise above 0°C. That's enough time for a quick stand-up routine, don't you think? Keep warm and enjoy the show!

First, let's calculate the heat required to raise the temperature of the ice from -18.7 °C to 0 °C. This can be done using the equation:

Q = mcΔT

Where:
Q = heat energy required
m = mass of the ice
c = specific heat of ice
ΔT = change in temperature

Given:
m = 0.540 kg
c = 2100 J/kg.K
ΔT = 0 °C - (-18.7 °C) = 18.7 °C

Substituting the values into the equation:

Q = (0.540 kg)(2100 J/kg.K)(18.7°C)
Q ≈ 20794.2 J

A) To find the time it takes before the ice starts to melt, we can use the formula:

time = heat energy supplied / heat supplied per unit time

Given:
heat supplied per unit time = 790 J/minute
heat energy supplied = 20794.2 J

Substituting the values into the formula:

time = 20794.2 J / 790 J/minute
time ≈ 26.3 minutes

Therefore, it takes approximately 26.3 minutes before the ice starts to melt.

B) To calculate the time it takes for the temperature to rise above 0 °C, we need to determine the heat energy required to melt the ice. This can be calculated using the formula:

Q = mL

Where:
Q = heat energy required
m = mass of the ice
L = heat of fusion for ice

Given:
m = 0.540 kg
L = 334 × 10^3 J/kg

Substituting the values into the formula:

Q = (0.540 kg)(334 × 10^3 J/kg)
Q ≈ 180360 J

Now, we can determine the time it takes using the formula:

time = heat energy required / heat supplied per unit time

Given:
heat supplied per unit time = 790 J/minute
heat energy required = 180360 J

Substituting the values into the formula:

time = 180360 J / 790 J/minute
time ≈ 228.5 minutes

Therefore, it takes approximately 228.5 minutes from the time heating begins for the temperature to rise above 0 °C.

To solve this problem, we need to calculate the heat needed to raise the temperature of the ice to 0°C and then the heat needed to melt the ice.

A) We know that the heat needed to raise the temperature of a substance can be calculated using the formula:

Q = mcΔT
where Q is the heat, m is the mass, c is the specific heat, and ΔT is the change in temperature.

In this case, the ice is initially at -18.7°C and needs to be raised to 0°C. The mass of the ice is 0.540 kg, and the specific heat of ice is 2100 J/kg.K. Substituting these values into the formula, we get:

Q = (0.540 kg) x (2100 J/kg.K) x (0°C - (-18.7°C))

Before the ice starts to melt, the heat supplied to the container is 790 J/minute. We can calculate the time by dividing the heat needed by the rate of heat supplied:

Time = Q / rate of heat supplied
= Q / (790 J/minute)

Substituting the value of Q, we can calculate the time in minutes.

B) Once all the ice has melted, the heat supplied will be used to raise the temperature of water from 0°C to some positive temperature. We can calculate the amount of heat needed to raise the temperature of the melted ice to a temperature above 0°C using the same formula:

Q = mcΔT

This time, the mass would be the total mass of melted ice, which is the same as the initial mass of the ice, 0.540 kg. The specific heat of water is also 2100 J/kg.K.

The temperature change ΔT would be the new desired temperature minus 0°C. We can calculate this difference and then find the time using the formula:

Time = Q / rate of heat supplied
= Q / (790 J/minute)

Substituting the values, we can calculate the time in minutes.

Remember to convert the time to hours, minutes, or any other required unit if needed.