(True or False) For an ideal gas, the specific enthalpy value (A) is a function of temperature only
The correct answer and explanation is :
True
For an ideal gas, the specific enthalpy value is indeed a function of temperature only. This concept is derived from the ideal gas law and the thermodynamic definition of enthalpy.
To understand this, we first need to consider the thermodynamic definition of enthalpy (H), which is: H=U+pVH = U + pV
Where:
- HH is the enthalpy,
- UU is the internal energy,
- pp is the pressure,
- VV is the volume.
For an ideal gas, the internal energy UU depends only on temperature, and the equation of state for an ideal gas pV=nRTpV = nRT (where nn is the number of moles and RR is the universal gas constant) relates pressure and volume. Because an ideal gas assumes no intermolecular forces and is composed of particles with negligible volume, its behavior is simplified.
The specific enthalpy hh (which is enthalpy per unit mass) can be written as: h=u+pvh = u + pv
Where:
- uu is the specific internal energy,
- pvpv is the pressure-volume product per unit mass.
For an ideal gas, the specific internal energy uu is a function of temperature only, which is typically expressed as: u(T)=∫Cv(T) dTu(T) = \int C_v(T) \, dT
Where Cv(T)C_v(T) is the specific heat at constant volume, which also depends on temperature. Similarly, the term pvpv can be rewritten as: pv=RTpv = RT
Thus, the specific enthalpy of an ideal gas can be written as: h(T)=u(T)+RTh(T) = u(T) + RT
Since both u(T)u(T) and RTRT depend only on temperature, we can conclude that the specific enthalpy of an ideal gas is a function of temperature only. This means that, for an ideal gas, knowing the temperature is sufficient to determine its specific enthalpy, and pressure or volume are not directly required.