Gases havea)only one value of specific heatb)two values of specific heatc)three values of specific heatd)no value of specific heate)under some conditions one value and sometimes two values of specific heatCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

A solid or a liquid when heated, does not undergo any change in the volume or pressure. But in case of a gas, both the pressure and volume change on heating. Therefore, specific heat of a gas is defined either at constant volume or at constant pressure and hence a gas has two specific heats.

Answer

Specific Heat of Gases

Gases have two values of specific heat, which are constant pressure specific heat (Cp) and constant volume specific heat (Cv).

Constant Pressure Specific Heat (Cp)

Cp is defined as the amount of heat required to raise the temperature of a unit mass of gas through one degree Celsius at a constant pressure. It is also known as the heat capacity at constant pressure. Cp is always greater than Cv for gases because when heat is added at constant pressure, the gas expands and does work against the external pressure. This means that some of the heat energy is used to do work rather than raise the temperature of the gas.

Constant Volume Specific Heat (Cv)

Cv is defined as the amount of heat required to raise the temperature of a unit mass of gas through one degree Celsius at a constant volume. It is also known as the heat capacity at constant volume. Cv is always less than Cp for gases because when heat is added at constant volume, the gas does not expand and no work is done against the external pressure. This means that all of the heat energy is used to raise the temperature of the gas.

Relationship between Cp and Cv

The relationship between Cp and Cv for gases is given by the specific heat ratio (γ) which is defined as the ratio of Cp to Cv. For monatomic gases, γ = 5/3, for diatomic gases, γ = 7/5, and for polyatomic gases, γ can vary between 1.33 and 1.67.

Applications of Cp and Cv

Cp and Cv are important thermodynamic properties of gases and are used in various engineering applications such as:

- Calculation of heat transfer in gas turbine engines
- Design of heat exchangers
- Calculation of gas flow rates in pipelines
- Analysis of combustion processes in engines.

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