Question

1. it takes 775 joules of energy to heat a 0.10 kg block of metal to 100°c from 10°c. what is the specific heat of the metal?

show your work

Explanation:

Step1: Recall the heat formula

The formula for heat energy is \( Q = mc\Delta T \), where \( Q \) is heat energy, \( m \) is mass, \( c \) is specific heat, and \( \Delta T \) is change in temperature.

Step2: Calculate temperature change

\( \Delta T = T_{final} - T_{initial} = 100^\circ C - 10^\circ C = 90^\circ C \).

Step3: Rearrange formula to solve for \( c \)

From \( Q = mc\Delta T \), we get \( c = \frac{Q}{m\Delta T} \).

Step4: Substitute values

Substitute \( Q = 775 \, J \), \( m = 0.10 \, kg \), and \( \Delta T = 90^\circ C \) into the formula: \( c = \frac{775}{0.10 \times 90} \).

Step5: Perform the calculation

\( 0.10 \times 90 = 9 \), then \( c = \frac{775}{9} \approx 86.11 \, J/(kg\cdot^\circ C) \).

Answer:

The specific heat of the metal is approximately \( 86.1 \, J/(kg\cdot^\circ C) \) (or more precisely \( \frac{775}{9} \approx 86.11 \, J/(kg\cdot^\circ C) \))