Answer :
Answer:
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