Question

A 0.050 kg metal bolt is heated to an unknown initial temperature. It is then dropped into calorimeter containing 0.15 kg of water with an initial temperature of 21.0°C. The bolt and the water then reach a final temperature of 25.0°C. If the metal has a specific heat capacity of 899 J/kg•°C, find the initial temperature of the metal.

Answer 1

The initial temperature of the metal bolt is 80.8 °C

We'll begin by calculating the heat absorbed by the water.

• Mass of water (M) = 0.15 Kg

• Initial temperature (T₁) = 21 °C

• Final temperature (T₂) = 25 °C

• Change in temperature (ΔT)  = T₂ – T₁ = 25 – 21 = 4 °C

• Specific heat capacity of water (C) = 4184 J/KgºC

• Heat absorbed (Q) =?

Q = MCΔT

Q = 0.15 × 4184 × 4

Q = 2510.4 J

Finally, we shall determine the initial temperature of the metal bolt.

• Heat absorbed by water = 2510.4 J

• Heat released by metal (Q) = –2510.4 J

• Mass of metal (M) = 0.050 Kg

• Final temperature (T₂) = 25 °C

• Specific heat capacity of metal (C) = 899 J/Kg°C

• Initial temperature (T₁) =?

Q = MC(T₂ – T₁)

–2510.4 = 0.050 × 899 (25 – T₁)

–2510.4 = 44.95 (25 – T₁)

Clear bracket

–2510.4 = 1123.75 – 44.95T₁

Collect like terms

–2510.4 – 1123.75 = –44.95T₁

–3634.15 = –44.95T₁

Divide both side by –44.95

T₁ = –3634.15 / –44.95

T₁ = 80.8 °C

Thus, the initial temperature of the metal is 80.8 °C.

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