Question

Thermodynamic values for water: heat of fusion = 3.34 x 10⁵ J/kg, heat of vaporization = 2.26 x 10⁶ J/kg, specific heat = 4180 J/kg·K. How can these values be used to calculate the amount of heat required to raise the temperature of a given mass of water?

Answer 1

To calculate the heat needed to raise the temperature of water, use the formula Q = mcΔT. For 275 g of water with 36.5 kJ of heat added, the temperature would increase by approximately 31.89°C. This example uses water's specific heat capacity of 4180 J/kg·K.

Step-by-step explanation:

The thermodynamic values for water can be utilized to calculate the amount of heat required to raise the temperature of a given mass of water using the formula Q = mcΔT, where Q is the heat added, m is the mass of the water, c is the specific heat capacity (4180 J/kg·K for water), and ΔT is the change in temperature. For example, to calculate the heat needed to raise the temperature of 275 g of water (note that 1 g = 0.001 kg), if 36.5 kJ of heat were added, we would convert 36.5 kJ to joules (36,500 J) and use Q = mcΔT to find ΔT: ΔT = Q/(mc) = 36,500 J / (0.275 kg × 4180 J/kg·K) = 31.89 K. This indicates the temperature of the water would increase by approximately 31.89°C.