How much heat is needed to heat 2 kg of water from 20°C to 100°C? (c = 4200 J/(kg·K)) — Physics problems | PhysLabo
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Heat needed to heat water

Easy 10 grade Molecular Physics and Thermodynamics / Internal Energy. Heat

How much heat is needed to heat water of mass $m = 2$ kg from a temperature of $t_1 = 20°$C to $t_2 = 100°$C? The specific heat capacity of water is $c = 4200$ J/(kg·K).

Given
  • $m = 2$ kg
  • $t_1 = 20°$C
  • $t_2 = 100°$C
  • $c = 4200$ J/(kg·K)
  • $Q = ?$
Hints
Hint 1 / 2
Heat for heating: $Q = cm\Delta t$.
Hint 2 / 2
Temperature difference: $100 - 20 = 80°$C.
Solution

Heat needed for heating:

$$Q = cm(t_2 - t_1) = 4200 \cdot 2 \cdot (100 - 20) = 4200 \cdot 2 \cdot 80$$

$$Q = 672\,000 \text{ J} = 672 \text{ kJ}$$

Answer

$Q = 672$ kJ (672 000 J)