A sample of water with a mass of 123.00 kg is heated from 25 C to 97 C. If the specific heat of water is [tex]$1 J-1 kg K -1$[/tex] then how much energy is required?
A. 11.93 kJ
B. 123.00 kJ
C. 15.01 kJ
D. 8.86 kJ
Answer (1)
Calculate the change in temperature: Δ T = 97 C − 25 C = 72 C .
Use the formula Q = m c Δ T to find the energy required.
Substitute the given values: Q = ( 123.00 kg ) × ( 1 J kg − 1 K − 1 ) × ( 72 K ) = 8856 J .
Convert Joules to kJ: Q = 8.856 kJ ≈ 8.86 kJ . The final answer is 8.86 kJ .
Explanation
Problem Analysis and Formula We are given a mass of water that is heated from an initial temperature to a final temperature. We need to find the amount of energy required for this process. We will use the formula for heat transfer: Q = m c Δ T , where Q is the heat energy, m is the mass, c is the specific heat, and Δ T is the change in temperature.
Calculating the Change in Temperature First, we need to find the change in temperature, which is the final temperature minus the initial temperature: Δ T = T f − T i = 97 C − 25 C = 72 C Since the change in temperature in Celsius is equal to the change in temperature in Kelvin, we can use this value directly in our calculations.
Calculating the Energy Required Now, we can calculate the energy required using the formula Q = m c Δ T :
Q = ( 123.00 kg ) × ( 1 J kg − 1 K − 1 ) × ( 72 K ) = 8856 J
Converting to kJ and Final Answer Finally, we convert the energy from Joules to kJ by dividing by 1000: Q = 1000 8856 J = 8.856 kJ Rounding to two decimal places, we get 8.86 kJ .
Examples
Imagine you're heating water for a large pot of pasta. Knowing the mass of the water, the initial and final temperatures, and the specific heat of water, you can calculate exactly how much energy your stove needs to supply. This principle is also crucial in industrial processes, like pasteurizing milk or sterilizing equipment, where precise temperature control and energy input are essential to ensure safety and quality.
