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If the specific heat of water is 4,186 J/kg∙°C, how much heat is required to increase the temperature of 1.2 kg of water from 23 °C to 39 °C?

Answer :

Answer:

8.0 × 10⁴ J

Explanation:

Step 1: Given data

  • Specific heat of water (c): 4,186 J/kg.°C
  • Mass of water (m): 1.2 kg
  • Initial temperature: 23 °C
  • Final temperature: 39 °C

Step 2: Calculate the change in the temperature

ΔT = 39 °C - 23 °C = 16 °C

Step 3: Calculate the heat required (Q)

We will use the following expression.

Q = c × m × ΔT

Q = 4,186 J/kg.°C × 1.2 kg × 16 °C

Q = 8.0 × 10⁴ J

Final answer:

The quantity of heat required to increase the temperature of 1.2 kg of water from 23 °C to 39 °C, given the specific heat of water used (4,186 J/kg∙°C), is approximately 80,467.2 Joules.

Explanation:

The heat required to change a material's temperature can be found using the formula: q = mcΔT, where q is the heat energy, m is the mass of the material, c is the material's specific heat, and ΔT is the change in temperature. Given that the specific heat (c) of water is 4,186 J/kg∙°C, the mass (m) of the water is 1.2 kg, and the temperature change (ΔT) is from 23 °C to 39 °C (a change of 16 °C), we can use the formula to find the required heat.

Substituting the given values into the formula: q = 1.2 kg * 4,186 J/kg∙°C * 16 °C. Calculating this gives an answer of approximately 80,467.2 Joules. Hence, this quantity of heat is required to increase the temperature of the water from 23 °C to 39 °C.

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