Question 4.17: Specific Heat How many calories are required to heat 352 g o...

Amount of heat = \text{SH} \times m \times \Delta T

Amount of heat = \text{SH} \times m \times (T_{2}-T_{1})\\ = \frac{1.00\ \text{cal}}{\cancel{\text{g}}\ .\ \cancel{\text{°C}}} \times 352\ \cancel{\text{g}} \times (95-23)\cancel{\text{°C}} \\ = 2.5 \times 10^{4}\ \text{cal}

Is this answer reasonable? Each gram of water requires one calorie to raise its temperature by one degree. We have approximately 350 g of water. To raise its temperature by one degree would therefore require approximately 350 calories. But we are raising the temperature not by one degree but by approximately 70 degrees (from 23 to 95). Thus, the total number of calories will be approximately 70 \times 350 = 24,500\ \text{cal}, which is close to the calculated answer. (Even though we were asked for the answer in calories, we should note that it will be more convenient to convert the answer to 25 kcal. We are going to see that conversion from time to time.)
■ Quick Check 4.17
How many calories are required to heat 731 g of water from 8°C to 74°C? Check your answer to see whether it is reasonable.