What is Specific Heat at Constant Pressure?

S7-SA4-0037

Grade Level:

Class 12

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Definition

What is it?

Specific heat at constant pressure (Cp) is the amount of heat energy needed to raise the temperature of one unit mass of a substance by one degree Celsius (or Kelvin), while keeping the pressure steady. It tells us how much heat a substance can absorb without changing its pressure.

Simple Example

Quick Example

Imagine you are making chai. If you heat milk in an open pan, the pressure inside the pan stays the same (atmospheric pressure). The amount of heat energy you need to add to raise the temperature of 1 kg of milk by 1°C is its specific heat at constant pressure. This is different from heating it in a pressure cooker, where the pressure changes.

Worked Example

Step-by-Step

PROBLEM: If 200 Joules of heat are added to 1 kg of a gas at constant pressure, and its temperature rises by 2°C, what is the specific heat at constant pressure (Cp) of the gas?
---STEP 1: Identify the given values.
Heat added (Q) = 200 Joules
Mass of gas (m) = 1 kg
Change in temperature (ΔT) = 2°C
---STEP 2: Recall the formula for specific heat at constant pressure.
Q = m * Cp * ΔT
---STEP 3: Rearrange the formula to solve for Cp.
Cp = Q / (m * ΔT)
---STEP 4: Substitute the values into the formula.
Cp = 200 J / (1 kg * 2°C)
---STEP 5: Calculate the result.
Cp = 200 J / 2 kg°C
Cp = 100 J/kg°C
---ANSWER: The specific heat at constant pressure (Cp) of the gas is 100 J/kg°C.

Why It Matters

Understanding specific heat at constant pressure is crucial for designing engines in EVs, optimizing rocket fuels in Space Technology, and even predicting climate patterns in Climate Science. Engineers use this concept to build efficient heating and cooling systems for homes and offices.

Common Mistakes

MISTAKE: Confusing specific heat at constant pressure (Cp) with specific heat at constant volume (Cv). | CORRECTION: Remember that Cp always considers work done against external pressure, making it generally larger than Cv.

MISTAKE: Forgetting to keep units consistent (e.g., mixing Joules with calories, or kg with grams). | CORRECTION: Always convert all quantities to standard SI units (Joules, kilograms, Kelvin or Celsius) before performing calculations.

MISTAKE: Assuming specific heat is constant for all temperature ranges. | CORRECTION: Specific heat can vary slightly with temperature, especially over very large temperature changes, though for most problems, we assume it's constant.

Practice Questions

Try It Yourself

QUESTION: 500 Joules of heat are added to 0.5 kg of a substance at constant pressure, raising its temperature by 5°C. What is its Cp? | ANSWER: 200 J/kg°C

QUESTION: A gas has a Cp of 800 J/kg°C. If 2 kg of this gas is heated at constant pressure and its temperature rises by 10°C, how much heat was added? | ANSWER: 16000 Joules

QUESTION: 1000 Joules of heat are supplied to 2 kg of a liquid at constant pressure, increasing its temperature from 20°C to 25°C. Calculate the specific heat at constant pressure of the liquid. | ANSWER: 100 J/kg°C

MCQ

Quick Quiz

Which of the following best describes specific heat at constant pressure?

Heat required to change phase at constant temperature.

Heat required to raise 1 kg of substance by 1 degree Celsius at constant pressure.

Heat required to raise 1 kg of substance by 1 degree Celsius at constant volume.

Total heat content of a substance.

The Correct Answer Is:

Specific heat at constant pressure (Cp) is defined as the heat needed to raise the temperature of a unit mass of a substance by one degree Celsius while keeping the pressure constant. Option C describes specific heat at constant volume.

Real World Connection

In the Real World

This concept is vital in designing air conditioning systems in your homes or offices. Engineers calculate Cp for different refrigerants to ensure the AC unit efficiently cools the room by absorbing heat without causing unwanted pressure changes in the system. It also helps in designing efficient cooking gas cylinders and pipelines.

Key Vocabulary

Key Terms

HEAT ENERGY: The transfer of thermal energy between systems due to a temperature difference. | CONSTANT PRESSURE: A condition where the external force per unit area on a system remains unchanged. | TEMPERATURE: A measure of the average kinetic energy of the particles in a substance. | UNIT MASS: A standard amount of mass, typically 1 kilogram (kg).

What's Next

What to Learn Next

Great job understanding Cp! Next, you should explore 'Specific Heat at Constant Volume (Cv)' and the relationship between Cp and Cv. This will help you understand how energy behaves in closed systems and open systems, which is super important in thermodynamics!