If 8.20 kJ of heat is needed to raise the temperature of a sample of metal from 12°C to 29°C, how many kilojoules of heat will be required to raise the temperature of the same sample of metal from 34°C to 57°C?

The heat needed is 11.1 kJ

Explanation:

Step 1: Data given

8.20 kJ of heat is needed

Initial temperature of metal = 12°C

Final temeprature of metal = 29 °C

Mass of the metal = unknown BUT the sample of metal has the same mass in both cases

Step 2: Define the formulas

Q1 = m*c * ΔT1

Q2 = m*c*ΔT2

The mass and the heat capacity are constant

Q1/Q2 = (m*c * ΔT1) / (m*c*ΔT2)

Q1/Q2 = ΔT1/ΔT2

Step 2: Calculate heat needed to raise from 34 to 57 °C

Q2 = (ΔT2 / ΔT1) * Q1

⇒ with Q2 = the heat need to raise the metal from 34 to 57 °C

⇒ with Q1 = the heat need to raise the metal from 12 to 29 °C = 8200 J

⇒ with ΔT2 = the change in temperature = 57° - 34 = 23 °C

⇒ with ΔT1 = the change in temperature = 29° - 12 = 17 °C

Q2 = (23/17) * 8200

Q2 = 11094 J = 11.1 kJ

The heat needed is 11.1 kJ