Answer:
2.2241 Kg
Explanation:
Given that it takes [tex]9.5 \times 10^5 \ J[/tex] of energy to convert a block of ice at −15° to water at 15°. Find the mass of the block of ice. We'll call [tex]9.5 \times 10^5 \ J[/tex] "[tex]Q_{melt}[/tex]" which is the total energy taken to melt the block of ice.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Heat energy formulas:}}\\Q=mc\Delta T\\Q=mL_f\\\end{array}\right}[/tex]
The energy it takes to raise the temperature of the ice from −15° to 0°:
[tex]Q_1=m_b(2090)(-15\°-0\°)\\\\||Q_1||=\boxed{31350m_b}[/tex]
The energy it takes to convert the ice to water:
[tex]Q_2=\boxed{3.33\times 10^5 m_b}[/tex]
The energy it takes to raise the temperature of the water from 0° to 15°:
[tex]Q_3=m_b(4186)(0\°-15\°)\\\\||Q_3||=\boxed{62790m_b}[/tex]
[tex]Q_{melt}=Q_1+Q_2+Q_3; \ Q_{melt}=9.5 \times 10^5 \\\\\Longrightarrow 9.5 \times 10^5=31350m_b+3.33\times 10^5 m_b+62790m_b\\\\\Longrightarrow 9.5 \times 10^5=(31350+3.33\times 10^5 +62790)m_b\\\\\Longrightarrow 9.5 \times 10^5=427140m_b\\\\\Longrightarrow \boxed{\boxed{m_b \approx 2.2241 \ kg}}[/tex]
Thus, the mass is found.
