Calculate the heat necessary to raise the temperature of 40.0 g of aluminum from 20.0 C to 700.0 C

We need 40.4 kJ to raise the temperature to 700.0 °C

Explanation:

Step 1: Data given

Mass of aluminium = 40.0 grams

Specific heat of aluminium = 0.900 J/g°C

The initial temperature = 20.0 °C

The final temperature = 700.0 °C

The melting point of aluminium = 660.3 °C

Step 2: Calculate heat needed to raise aluminium from 20.0 °C to 660.3 °C

Q = m*C*ΔT

⇒with Q = the heat needed = TO BE DETERMINED

⇒with m =the mass of aluminium = 40.0 grams

⇒with c = the specific heat of aluminium = 0.90 J/g°C

⇒with ΔT = the change of temperature = T2 - T1 = 660.3 - 20.0 = 640.3 °C

Q = 40.0 * 0.900 * 640.3

Q = 23050.8 J

Step 3: Calculate heat need to melt aluminium

Q = m*ΔHfusion

Q = 40.0 g*398 J/g

Q = 15920 J

Step 4: Calculate heat needed to raise aluminium from 660.3 to 700.0°C

Q = m*C*ΔT

⇒with Q = the heat needed = TO BE DETERMINED

⇒with m =the mass of aluminium = 40.0 grams

⇒with c = the specific heat of aluminium = 0.90 J/g°C

⇒with ΔT = the change of temperature = T2 - T1 = 700 - 660.3 = 39.7 °C

Q = 40.0 * 0.90 * 39.7

Q = 1429.2 J

Step 5: Calculate the total heat needed

Q = 23050.8 + 15920 + 1429.2

Q = 40400 J = 40.4 kJ

We need 40.4 kJ to raise the temperature to 700.0 °C