Question

The addition of 9.5×10^5 of thermal energy is required to convert a block of ice at −15° to water at 15°. What was the mass of the block of ice?

Answer 1

2.2241 Kg

Step-by-step explanation:

Given that it takes
`9.5 * 10^5 \ J` 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
`9.5 * 10^5 \ J` "
`Q_(melt)`" which is the total energy taken to melt the block of ice.

`\boxed{\left\begin{array}{ccc}\text{\underline{Heat energy formulas:}}\\Q=mc\Delta T\\Q=mL_f\\\end{array}\right}`

The energy it takes to raise the temperature of the ice from −15° to 0°:

`Q_1=m_b(2090)(-15\°-0\°)\\\\||Q_1||=\boxed{31350m_b}`

The energy it takes to convert the ice to water:

`Q_2=\boxed{3.33* 10^5 m_b}`

The energy it takes to raise the temperature of the water from 0° to 15°:

`Q_3=m_b(4186)(0\°-15\°)\\\\||Q_3||=\boxed{62790m_b}`

`Q_(melt)=Q_1+Q_2+Q_3; \ Q_(melt)=9.5 * 10^5 \\\\\Longrightarrow 9.5 * 10^5=31350m_b+3.33* 10^5 m_b+62790m_b\\\\\Longrightarrow 9.5 * 10^5=(31350+3.33* 10^5 +62790)m_b\\\\\Longrightarrow 9.5 * 10^5=427140m_b\\\\\Longrightarrow \boxed{\boxed{m_b \approx 2.2241 \ kg}}`

Thus, the mass is found.