What is Specific Heat at Constant Volume?

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Grade Level:

Class 12

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Definition

What is it?

Specific heat at constant volume (Cv) is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius (or Kelvin) while keeping its volume fixed. Imagine heating water in a completely sealed, unmoving container – the volume doesn't change. It tells us how much heat a substance can 'hold' under this specific condition.

Simple Example

Quick Example

Think about cooking dal in a pressure cooker. When the lid is sealed, the volume inside is constant. The specific heat at constant volume for the ingredients inside tells us how much heat energy is needed to raise their temperature by one degree without letting them expand. If you needed 100 Joules to heat 1 kg of water by 1 degree Celsius in a sealed container, then Cv for water would be 100 J/kg°C.

Worked Example

Step-by-Step

QUESTION: 2 kg of a gas is heated in a rigid (fixed volume) container. Its temperature increases from 25°C to 30°C. If the specific heat at constant volume (Cv) for this gas is 0.7 kJ/kg°C, how much heat energy was supplied?

Step 1: Identify the given values.
Mass (m) = 2 kg
Change in temperature (ΔT) = 30°C - 25°C = 5°C
Specific heat at constant volume (Cv) = 0.7 kJ/kg°C

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Step 2: Recall the formula for heat energy at constant volume.
Q = m * Cv * ΔT

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Step 3: Substitute the values into the formula.
Q = 2 kg * 0.7 kJ/kg°C * 5°C

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Step 4: Calculate the heat energy.
Q = 2 * 0.7 * 5
Q = 1.4 * 5
Q = 7 kJ

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ANSWER: The heat energy supplied was 7 kJ.

Why It Matters

Understanding specific heat at constant volume is crucial for designing engines in EVs, rockets in Space Technology, and even for climate models in Climate Science. Engineers use this concept to predict how materials will behave under extreme heat without changing their size, which is vital for safe and efficient operations. This knowledge helps create everything from better air conditioners to safer spacecraft.

Common Mistakes

MISTAKE: Confusing specific heat at constant volume (Cv) with specific heat at constant pressure (Cp). | CORRECTION: Remember Cv applies when the volume is fixed (like in a sealed tank), while Cp applies when pressure is fixed (like heating water in an open pot). They are different values.

MISTAKE: Using the wrong units for temperature change (e.g., using Celsius for absolute temperature in some formulas). | CORRECTION: For specific heat, a change of 1 degree Celsius is the same as a change of 1 Kelvin, so ΔT can be in °C or K. However, ensure consistency with the units given for Cv.

MISTAKE: Forgetting that specific heat is per unit mass. | CORRECTION: Always multiply by the total mass (m) of the substance when calculating the total heat energy (Q). The 'per kg' in Cv means you need to account for the total kilograms.

Practice Questions

Try It Yourself

QUESTION: 5 kg of a gas in a closed container has its temperature raised by 10°C. If its Cv is 0.5 kJ/kg°C, how much heat was added? | ANSWER: 25 kJ

QUESTION: A 3 kg block of metal is heated in a rigid chamber. If 90 kJ of heat is supplied and its Cv is 0.6 kJ/kg°C, what is the change in its temperature? | ANSWER: 50°C

QUESTION: 200 grams of a liquid is heated from 20°C to 40°C in a sealed flask. If 4000 Joules of heat were supplied, calculate the specific heat at constant volume (Cv) for this liquid in J/kg°C. (Hint: Convert grams to kilograms first!) | ANSWER: 1000 J/kg°C

MCQ

Quick Quiz

What does specific heat at constant volume (Cv) primarily measure?

The heat required to change the state of a substance.

The heat required to raise the temperature of a unit mass at fixed volume.

The heat required to raise the temperature of a unit mass at fixed pressure.

The work done by a gas during expansion.

The Correct Answer Is:

Specific heat at constant volume (Cv) specifically deals with the heat needed to change temperature when the volume does not change. Option C describes specific heat at constant pressure (Cp), and options A and D are related to other thermodynamic concepts.

Real World Connection

In the Real World

In India, specific heat at constant volume is critical in the design of gas cylinders for domestic use (LPG) or industrial applications. Engineers calculate how much heat these gases can absorb without expanding, ensuring the cylinders can safely contain them even when heated by the environment. This prevents accidents and ensures safe transportation and storage, impacting millions of households and industries daily.

Key Vocabulary

Key Terms

SPECIFIC HEAT: The amount of heat needed to raise the temperature of a unit mass of a substance by one degree | CONSTANT VOLUME: A process where the space occupied by a substance does not change | HEAT ENERGY: The transfer of thermal energy between objects due to a temperature difference | TEMPERATURE: A measure of the average kinetic energy of the particles within a substance

What's Next

What to Learn Next

Next, you should explore 'Specific Heat at Constant Pressure (Cp)'. Understanding Cp will help you see how heat behaves when substances can expand, and then you can learn about the relationship between Cv and Cp, which is a fundamental concept in thermodynamics!