Define specific heat at constant volume and specific heat at constant pressure.

Short Answer

Specific heat at constant volume (Cv) and specific heat at constant pressure (Cp) are two types of specific heat capacities that describe how a substance absorbs heat.

Specific heat at constant volume (Cv) is the amount of heat required to raise the temperature of a unit mass of a substance by 1°C while keeping the volume constant. Specific heat at constant pressure (Cp) is the amount of heat required to raise the temperature of a unit mass of a substance by 1°C while keeping the pressure constant. These properties are essential in thermodynamics for analyzing heat transfer in gases and fluids.

Detailed Explanation

Specific Heat at Constant Volume (Cv)

Specific heat at constant volume (Cv) refers to the heat required to raise the temperature of a unit mass of a substance while maintaining a constant volume. Since the volume is fixed, no work is done, and all the heat supplied increases the internal energy of the substance.

Formula for Cv

Q=mCvΔTQ = m C_v \Delta TQ=mCv​ΔT

Where:

  • QQQ = heat energy added (Joules)
  • mmm = mass of the substance (kg)
  • CvC_vCv​ = specific heat at constant volume (J/kg·K)
  • ΔT\Delta TΔT = temperature change (K)

Key Characteristics of Cv

  • Used in rigid containers where volume does not change (e.g., closed piston cylinders).
  • No expansion work is done, so all heat goes into increasing internal energy.
  • Commonly used in thermodynamic cycles involving gases.

Examples of Cv Applications

  • Internal combustion engines where air-fuel mixtures heat up at constant volume.
  • Gas-filled containers where temperature changes without volume expansion.

Specific Heat at Constant Pressure (Cp)

Specific heat at constant pressure (Cp) refers to the heat required to raise the temperature of a unit mass of a substance while maintaining a constant pressure. Since pressure remains constant, heat energy is used for both raising the temperature and doing expansion work.

Formula for Cp

Q=mCpΔTQ = m C_p \Delta TQ=mCp​ΔT

Where:

  • QQQ = heat energy added (Joules)
  • mmm = mass of the substance (kg)
  • CpC_pCp​ = specific heat at constant pressure (J/kg·K)
  • ΔT\Delta TΔT = temperature change (K)

Key Characteristics of Cp

  • Used in open systems, where pressure remains constant (e.g., atmospheric heating).
  • Heat energy is divided into raising internal energy and expansion work.
  • Cp is always greater than Cv because of the additional work done by the system.

Examples of Cp Applications

  • Air conditioning and heating systems, where air expands while absorbing heat.
  • Boilers and steam power plants, where heat transfer occurs at constant pressure.
Conclusion

Specific heat at constant volume (Cv) refers to heat energy required to raise temperature while keeping volume constant, whereas specific heat at constant pressure (Cp) refers to heat energy needed to raise temperature while keeping pressure constant. Cp is always greater than Cv because it includes both temperature increase and expansion work. These concepts are crucial in heat transfer, thermodynamics, and mechanical engineering applications