b. How much energy is required to heat 550 g of iron (c_(iron)=0.449J/g^circ C) initially at 20^circ C to 100^circ C

To calculate the energy required to heat a substance, we can use the formula for heat energy:<br /><br />\[ Q = mc\Delta T \]<br /><br />where:<br />- \( Q \) is the heat energy (in joules),<br />- \( m \) is the mass of the substance (in grams),<br />- \( c \) is the specific heat capacity of the substance (in joules per gram per degree Celsius),<br />- \( \Delta T \) is the change in temperature (in degrees Celsius).<br /><br />Given:<br />- Mass of iron, \( m = 550 \, \text{g} \)<br />- Specific heat capacity of iron, \( c = 0.449 \, \text{J/g}^{\circ}\text{C} \)<br />- Initial temperature, \( T_{\text{initial}} = 20^{\circ}\text{C} \)<br />- Final temperature, \( T_{\text{final}} = 100^{\circ}\text{C} \)<br /><br />First, calculate the change in temperature (\( \Delta T \)):<br /><br />\[ \Delta T = T_{\text{final}} - T_{\text{initial}} = 100^{\circ}\text{C} - 20^{\circ}\text{C} = 80^{\circ}\text{C} \]<br /><br />Now, substitute the values into the formula:<br /><br />\[ Q = (550 \, \text{g}) \times (0.449 \, \text{J/g}^{\circ}\text{C}) \times (80^{\circ}\text{C}) \]<br /><br />\[ Q = 550 \times 0.449 \times 80 \]<br /><br />\[ Q = 19736 \, \text{J} \]<br /><br />Therefore, the energy required to heat 550 g of iron from \(20^{\circ}\text{C}\) to \(100^{\circ}\text{C}\) is 19,736 joules.