Math Problem Statement

Calculate the amount of energy in joules that must be added to 245.0 g of ice at -45.0 ºC to

turn it all into liquid water at 0.00 ºC. Hint, two separate calculations must be done and then

added together.

Solution

To calculate the energy required to convert 245.0 g of ice at 45.0 C-45.0\ ^\circ\text{C} to liquid water at 0.00 C0.00\ ^\circ\text{C}, we need to break the problem into two parts:

  1. Heating the ice from 45.0 C-45.0\ ^\circ\text{C} to 0.0 C0.0\ ^\circ\text{C}.
  2. Melting the ice at 0.0 C0.0\ ^\circ\text{C} to turn it into liquid water.

Step 1: Heating the ice

To calculate the heat required to raise the temperature of ice from 45.0 C-45.0\ ^\circ\text{C} to (0.0\ ^\circ\text{C}\

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Math Problem Analysis

Mathematical Concepts

Thermodynamics
Heat Transfer
Phase Change

Formulas

q = mcΔT (Heat required to change the temperature of a substance)
q = mL_f (Heat required to melt ice)

Theorems

First Law of Thermodynamics

Suitable Grade Level

Grades 11-12 (Physics or Chemistry)