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Example 9.17: A piece of iron of mass 2.0kg has a thermal capacity of 966J^(@)C^(-1). (a) How much heat is needed to warm it by 15^(@)C ? (b) What is its specific heat capacity in SI units?

Example 99.1717: A piece of iron of mass 2.0 kg 2.0 \mathrm{~kg} has a thermal capacity of 966 J∘C−1 966 \mathrm{~J}^{\circ} \mathrm{C}^{-1} .\newline(a) How much heat is needed to warm it by 15∘C 15^{\circ} \mathrm{C} ?\newline(b) What is its specific heat capacity in SI units?

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Full solution

Q. Example 99.1717: A piece of iron of mass 2.0 kg 2.0 \mathrm{~kg} has a thermal capacity of 966 J∘C−1 966 \mathrm{~J}^{\circ} \mathrm{C}^{-1} .\newline(a) How much heat is needed to warm it by 15∘C 15^{\circ} \mathrm{C} ?\newline(b) What is its specific heat capacity in SI units?
  1. Use formula Q=mcΔTQ = mc\Delta T: To find the heat needed, use the formula Q=mcΔTQ = mc\Delta T, where mm is mass, cc is specific heat capacity, and ΔT\Delta T is the change in temperature.
  2. Plug in values: Plug in the values: Q=(2.0 kg)(966 J/kg∘C)(15∘C)Q = (2.0 \, \text{kg})(966 \, \text{J/kg}^\circ\text{C})(15^\circ\text{C}).
  3. Calculate heat: Calculate the heat: Q=2.0×966×15=28980 J.Q = 2.0 \times 966 \times 15 = 28980 \, \text{J}.
  4. Find specific heat capacity: Now, to find the specific heat capacity in SI units, we need to divide the thermal capacity by the mass.
  5. Calculate specific heat capacity: Calculate the specific heat capacity: c=966 J/°C2.0 kgc = \frac{966 \, \text{J}/\degree\text{C}}{2.0 \, \text{kg}}.
  6. Calculate specific heat capacity: Calculate the specific heat capacity: c=966 J/°C2.0 kgc = \frac{966 \, \text{J}/°\text{C}}{2.0 \, \text{kg}}. Perform the division: c=483 J/kg°C.c = 483 \, \text{J/kg}°\text{C}.

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