How much energy is required to raise the temperature of 11.1 grams of solid chromium from 24.3^circ C to 36.9^circ C

To calculate the energy required to raise the temperature of a substance, we can use the formula:<br /><br />\[ Q = mc\Delta T \]<br /><br />where:<br />- \( Q \) is the energy required,<br />- \( m \) is the mass of the substance,<br />- \( c \) is the specific heat capacity of the substance,<br />- \( \Delta T \) is the change in temperature.<br /><br />Given:<br />- \( m = 11.1 \) grams,<br />- Initial temperature \( T_{\text{initial}} = 24.3^{\circ}C \),<br />- Final temperature \( T_{\text{final}} = 36.9^{\circ}C \).<br /><br />First, calculate the change in temperature (\( \Delta T \)):<br /><br />\[ \Delta T = T_{\text{final}} - T_{\text{initial}} \]<br />\[ \Delta T = 36.9^{\circ}C - 24.3^{\circ}C \]<br />\[ \Delta T = 12.6^{\circ}C \]<br /><br />Next, we need the specific heat capacity (\( c \)) of solid chromium. The specific heat capacity of solid chromium is approximately \( 0.449 \, \text{J/g}^{\circ}\text{C} \).<br /><br />Now, plug in the values into the formula:<br /><br />\[ Q = mc\Delta T \]<br />\[ Q = 11.1 \, \text{g} \times 0.449 \, \text{J/g}^{\circ}\text{C} \times 12.6^{\circ}\text{C} \]<br /><br />Calculate \( Q \):<br /><br />\[ Q = 11.1 \times 0.449 \times 12.6 \]<br />\[ Q = 64.5 \, \text{J} \]<br /><br />Therefore, the energy required to raise the temperature of 11.1 \( 24.3^{\circ}C \) to \( 36.9^{\circ}C \) is approximately \( 64.5 \) joules.