Specific Heat at Constant Volume

Definition

Specific heat at constant volume is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius while maintaining a constant volume. This property is crucial for understanding how internal energy changes with temperature in a system where no work is done due to volume change, making it an essential concept in thermodynamics.

5 Must Know Facts For Your Next Test

1. Specific heat at constant volume (denoted as $$C_v$$) is typically lower than specific heat at constant pressure (denoted as $$C_p$$) for a given substance.
2. For an ideal gas, the specific heat at constant volume can be related to changes in internal energy through the equation $$ ext{d}U = nC_v ext{d}T$$.
3. In isentropic processes, changes in temperature and pressure are directly related through specific heats, where $$C_v$$ plays a key role in determining the behavior of the gas.
4. The ratio of specific heats, $$rac{C_p}{C_v}$$, is known as the adiabatic index or heat capacity ratio, and it significantly impacts the efficiency of thermodynamic cycles.
5. Specific heat at constant volume is particularly important in analyzing systems with rigid boundaries where no work is done on or by the system.

Review Questions

• How does specific heat at constant volume influence internal energy changes in a closed system?
  • Specific heat at constant volume directly affects internal energy changes in a closed system because when heat is added without changing the volume, the internal energy increases. The relationship is given by the formula $$ ext{d}U = nC_v ext{d}T$$, which indicates that the change in internal energy (U) is proportional to the specific heat at constant volume (C_v), the number of moles (n), and the change in temperature (dT). Therefore, understanding C_v helps predict how energy is stored within a system when volume remains unchanged.
• Discuss how specific heat at constant volume relates to the behavior of gases during isentropic processes.
  • In isentropic processes, which are adiabatic and reversible, specific heat at constant volume plays a vital role in determining how gases respond to changes in pressure and temperature. For an ideal gas undergoing an isentropic process, relationships involving specific heats allow us to derive equations that relate temperature and pressure. The specific heat at constant volume affects how much energy must be added or removed to change the temperature without altering volume, which is essential for calculating efficiencies in thermodynamic cycles like those found in engines.
• Evaluate how differences between specific heat at constant volume and constant pressure impact thermodynamic efficiency in real-world applications.
  • The differences between specific heat at constant volume and constant pressure significantly impact thermodynamic efficiency in applications such as engines and refrigeration systems. In practical situations, knowing both $$C_v$$ and $$C_p$$ allows engineers to optimize cycle performance by managing energy transformations effectively. For example, when designing an engine cycle, using the correct specific heats helps determine work output and heat transfer efficiency, ultimately influencing fuel consumption and power generation. This understanding ensures that systems operate more efficiently under varying conditions.

Related terms

Internal Energy: The total energy contained within a system, which includes both kinetic and potential energy of the particles.

Enthalpy:

A thermodynamic quantity equivalent to the internal energy of a system plus the product of its pressure and volume, often used to analyze processes at constant pressure.

Specific Heat at Constant Pressure: The amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius while maintaining constant pressure.