An open container holds ice of mass 0.515kg at a temperature of -16.7C. The mass of the container can be ignored. Heat is supplied to the container at the constant rate of 700J/Minute. The specific...

An open container holds ice of mass 0.515kg at a temperature of -16.7C. The mass of the container can be ignored. Heat is supplied to the container at the constant rate of 700J/Minute.

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

How much time passes before ice starts to melt in minutes?

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

Asked on by user4787695

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t-nez | High School Teacher | (Level 3) Associate Educator

Posted on

You solve this problem by calculating the heat needed to bring the temperature of the ice fro -16.7 degrees C up to 0 degrees C, and then calculating the heat needed to melt the ice. Knowing how much heat is added per minute you can calculate how long each step will take. The temperature will begin to rise above 0 degrees C when all of the ice has melted.

For the first step, the heat aborbed is q=mc `Delta` T ` <br> `

q = (0.515 kg)(2100 J/kg-deg C)[0 deg C- (-16.7 deg C)] = 18,061 J

At 700 Joules added per minute the time it would take to reach this temperature is:

(18061 J)/700 J/min) = 25.8 minutes until 0 deg C is reached and ice starts to melt

For the second step, the heat absorbed in melting the ice is:

`Delta` H = mass x heat of fusion

 = (0.515 kg)(334,000 J/kg) = 172,000 J

The time this would take is (172,000 J)/(700 J/min) = 246 min

Total minutes = 25.8 + 246 = 272 minutes until ice melts and temperature begins to go above 0 deg C

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