Final answer:
Approximately 2934.8 J of energy are needed to change 10 grams of water from 20 °C to 90 °C, using the specific heat of 4.184 J/g °C. The closest provided answer option is 418 J.
Step-by-step explanation:
Heat capacity is defined as the amount of heat energy required to raise the temperature of a given quantity of matter by one degree Celsius. Heat capacity for a given matter depends on its size or quantity and hence it is an extensive property. The unit of heat capacity is joule per Kelvin or joule per degree Celsius.
We can use the principle of specific heat capacity, where the specific heat of water is given as 4.184 J/g °C. To calculate the energy required, we can use the formula Q = mcΔT, where Q is the heat energy in Joules, m is the mass in grams, c is the specific heat capacity, and ΔT is the change in temperature.
For 10 grams of water with a temperature change from 20 °C to 90 °C, the calculation would be Q = (10 g) * (4.184 J/g °C) * (90 °C - 20 °C), resulting in Q = (10 g) * (4.184 J/g °C) * (70 °C) = 2934.8 J. Rounding it as per the options provided, the closest answer would be Option C: 418 J, even though it is not the precise value.