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Chapter 2: Problem 119

How much heat energy is 1 cal? Give your answer in terms of changing the temperature of water.

Short Answer

Expert verified
1 calorie of heat energy is equivalent to raising the temperature of 1 gram of water by 1 degree Celsius, so 1 cal = 1 °C temperature change for 1 gram of water.

Step by step solution

01

Understand the definition of calorie

A calorie is a unit of heat energy. It is defined as the amount of heat energy required to raise the temperature of 1 gram of water by 1 degree Celsius.
02

Identify the specific heat of water

The specific heat of water is the amount of heat per unit mass needed to raise the temperature by 1 degree Celsius. For water, the specific heat is 1 cal/g°C. This means that 1 calorie of heat energy will raise the temperature of 1 gram of water by 1 degree Celsius.
03

Calculate the temperature change

We have 1 calorie of heat energy, and we know that the specific heat of water is 1 cal/g°C. So, we can calculate the temperature change (ΔT) for 1 gram of water using the formula: ΔT = Heat energy / (mass x specific heat) where the mass of water = 1 g, and the specific heat of water = 1 cal/g°C. Plugging these values into the formula, we get: ΔT = 1 cal / (1 g × 1 cal/g°C) = 1 °C
04

Express the answer in terms of changing the temperature of water

Now we know that 1 calorie of heat energy is equivalent to raising the temperature of 1 gram of water by 1 degree Celsius. Therefore, 1 cal = 1 °C temperature change for 1 gram of water.

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