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Chapter 14: Problem 12

If \(125.6 \mathrm{kJ}\) of heat are supplied to \(5.00 \times 10^{2} \mathrm{g}\) of water at \(22^{\circ} \mathrm{C},\) what is the final temperature of the water?

Short Answer

Expert verified
Answer: The final temperature of the water is approximately 81.88掳C.

Step by step solution

01

Convert the heat energy from kJ to J

Since 1 kJ = 1000 J, convert 125.6 kJ to J: 125.6 kJ 脳 1000 = 125600 J
02

Calculate the heat absorbed by the water

To calculate the heat absorbed by the water, we use the formula: Q = mc螖T Where Q is the heat absorbed, m is the mass of the water, c is the specific heat capacity of water, and 螖T is the change in temperature. We are given the mass of water and its initial temperature. We also know that the specific heat capacity of water is about 4.18 J/g掳C. We will solve for 螖T to find the final temperature: 螖T = Q / (mc)
03

Substitute the given values into the formula

Substitute the values into the formula with m = 5.00 x 10^2 g, c = 4.18 J/g掳C, and Q = 125600 J: 螖T = 125600 J / ( (5.00 x 10^2 g) x 4.18 J/g掳C)
04

Calculate the change in temperature (螖T)

Perform the calculations: 螖T 鈮� 59.88掳C
05

Determine the final temperature of the water

To find the final temperature, add the change in temperature (螖T) to the initial temperature (22掳C): Final temperature = Initial temperature + 螖T Final temperature = 22掳C + 59.88掳C Final temperature 鈮� 81.88掳C The final temperature of the water is approximately 81.88掳C.

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