Question

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

Short answer

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

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.

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.

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

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.

Key concepts

Heat Energy

Heat energy is a form of energy that travels from a warmer object to a cooler one. It is measured in units called calories. When you heat an object, you're transferring energy to it, causing its molecules to move faster. This movement increases the object's temperature.

• Heat energy flows naturally from hot to cold.
• A calorie is a specific measurement of this heat energy.

Understanding heat energy helps in various scientific fields, such as thermodynamics and physical chemistry. It is crucial for understanding processes like cooking, heating, and even weather patterns.

Specific Heat of Water

The specific heat of a substance refers to how much energy in the form of heat is needed to change the temperature of 1 gram of the substance by 1 degree Celsius. Water is unique because it has a high specific heat—a whopping 1 cal/g°C. This value means that water can absorb a lot of heat without a significant temperature change.

• High specific heat contributes to water's role in climate regulation.
• It affects how water is used in everyday tasks like cooking and temperature control.

The high specific heat of water is why coastal areas tend to have milder climates. Water absorbs heat throughout the day and releases it slowly, moderating temperature changes.

Temperature Change

Temperature change involves altering the thermal state of a substance, usually by adding or removing heat. In the formula \[ΔT = \frac{\text{Heat energy}}{\text{mass} \times \text{specific heat}}\]ΔT represents the change in temperature. This equation shows how heat, mass, and specific heat work together to determine how much the temperature will shift.

• If the specific heat is high, temperature changes are slow.
• Low specific heat means quicker temperature changes for the same amount of heat.

You can calculate temperature change using known values of heat energy and specific heat. This understanding is key in scenarios ranging from cooking to industrial applications.

Measurement of Heat

Measurement of heat is essential for a wide range of applications, from scientific research to everyday tasks like heating your home. Heat is typically measured in calories or joules, but here we're focusing on calories. One calorie is the amount of heat needed to increase the temperature of 1 gram of water by 1 degree Celsius.

• This unit of measurement is crucial for scientific experiments.
• It aids in understanding how substances absorb and emit heat.

With heat measurement, you can calculate things like energy efficiency in appliances and even track metabolic rates in nutrition science.