Constant pressure, heat capacity

Heat Capacity. The multiple property estimation methods for constant pressure ideal-gas heat capacities cover a broad range of organic compounds (188,216,217). Joback s method (188) is the easiest to use however, usage of all these methods has been recommended only over the range 280—1100 K (7). An accurate method for ideal-gas heat capacities (constant pressure), limited to hydrocarbons, has been presented (218) that involves a fit of seven variables, and includes steric, ring, branching, alkene, and even allene corrections. 

AH = Actual available energy, Btu/lb Cp = Heat capacity (constant pressure), Btu/lb °F Ti = Inlet temperature, °R Pi, P2 = Inlet, oudet pressures, psia K = Cp/C,... 

The following table gives the properties of common gas chromatographic carrier gases. These properties are those used most often in designing separation and optimizing detector performance. The density values are determined at CPC and 0.101 MPa (760 torr).1 The thermal conductivity values, X, are determined at 48.9°C (120°F).1 The viscosity values are determined at the temperatures listed and at 0.101 MPa (760 torr).1 The heat capacity (constant pressure) values are determined at 15°C and 0.101 MPa (750 torr).2... 

SV40 transformed African green monkey kidney cells Heat capacity (constant pressure)... 

Cp ad = heat capacity (constant pressure) of adsorbate Cp i = the heat capacity at constant pressure for the liquid phase of adsorptive d = distance D = tube diameter... 

CD = tube length for vaporization, ft. Figure 10-110. c or Cp = heat capacity or specific heat at constant pressure, Btu/lb(°F) or, heat capacity of condensate, pcu/lb(°C)... 

When a substance is heated at constant pressure without change of phase through a temperature rise dr the heat absorbed is Cp dr, where Cp is the molar heat capacity at constant pressure, and the entropy increase is... 

Whereas heat capacity is a measure of energy, thermal diffusivity is a measure of the rate at which energy is transmitted through a given plastic. It relates directly to processability. In contrast, metals have values hundreds of times larger than those of plastics. Thermal diffusivity determines plastics rate of change with time. Although this function depends on thermal conductivity, specific heat at constant pressure, and density, all of which vary with temperature, thermal diffusivity is relatively constant. 

The heat capacity of a substance can differ, depending on which are the variables held constant, with the quantity being held constant usually being denoted with a subscript. For example, the specific heat at constant pressure is commonly denoted cP, while the specific heat at constant volume is commonly denoted cv ... 

A fire occurs in a space station at 200 kW. The walls can be considered adiabatic and of negligible heat capacity. The initial and fuel temperatures are at 25 °C. Assume the station atmosphere has uniform properties with constant specific heats as given. Assume that the constant and equal specific heats of constant pressure and volume are 1.2 and 1.0 kJ/kg K respectively. Conduct your analysis for the control volume (CV) consisting of the station uniform atmosphere, excluding all solids and the fuel in its solid state. 

These two expressions differ only by the leading constant terms. The simple thermal conductivity expression derived here is roughly 40% the size of the rigorous result. It captures the functional dependence on temperature, molecular mass, heat capacity, and pressure (independent of pressure) of the exact result. Experimentally the thermal conductivity is generally found to be independent of pressure, except at very low pressures. The thermal conductivity is predicted to increase as the square root of temperature, which somewhat underestimates the actual temperature dependence. Consideration of interactions between molecules, as in the next section, brings the temperature dependence into better accord with observation. 

The term Cp is the heat capacity of the gas at constant pressure it is related to the energy required to overcome molecular attraction as the gas expands due to heating at constant pressure. 

Under isentropic conditions and with constant heat capacities, the pressure-volume relation is... 

The equation of state-does not include all the experimental information which we must have about a system or substance. Ve need to tnow also its heat, capacity or specific heat, as a function of temperature. Suppose, for instance, that we know the specific heat at constant pressure Cp as a function of temperature at a particular pressure. Then we can find the difference of internal energy, or of entropy, between any two states. From the first state, we can go adiabatically to the pressure at which we know Cp, In this process, since no heat is absorbed, the change of internal energy equals the work done, which we can compute from the equation of state. Then we absorb heat at constant pressure, until we reach the point from which another adiabatic process will carry us to the desired end point. The change of internal energy can be found for the process at constant pressure, since there we know CP) from which we can... 

After writing mass balances, energy balances, and equilibrium relations, we need system property data to complete the formulation of the problem. Here, we divide the system property data into thermodynamic, transport, transfer, reaction properties, and economic data. Examples of thermodynamic properties are heat capacity, vapor pressure, and latent heat of vaporization. Transport properties include viscosity, thermal conductivity, and difiusivity. Corresponding to transport properties are the transfer coefficients, which are friction factor and heat and mass transfer coefficients. Chemical reaction properties are the reaction rate constant and activation energy. Finally, economic data are equipment costs, utility costs, inflation index, and other data, which were discussed in Chapter 2. 

The specific enthalpy of a species H — 0 PV) also increases with increasing emper-ature. If a species is heated at constant pressure and H is plotted versus T. the slope of the resulting curve is the heat capacity at constant pressure of the species. Cp[T). or = ( f / r)consiant p- It follows that if a gas undergoes a change in temperature from T- to Tz. with or without a concurrent change in pressure. 

The actual change of heat capacity with pressure is given by an expression obtained by the integration of equation (21.11). At a sufficiently low pressure, represented by P, where the gas behaves ideally, the heat capacity Cp may be regarded as virtually independent of pressure this pressure may be taken as the lower limit of integration, and if the upper limit is any pressure P at which the heat capacity at constant pressure is Cp, then... 

Specific heat. The ratio of the heat capacity of a substance to the heat capacity of water, or the quantity of heat required for a 1 degree temperature change in a unit weight of material. Commonly expressed in Btu/lb/degree F or in cal/g/degree. For gas, the specific heat at constant pressure is greater than that at constant volume by the amount of heat needed for expansion. 

Cl = average liquid specific heat capacity, J/Kg.K Cp = specific heat at constant pressure, J/Kg.K d - vent diameter, mm F = flow reduction factor... 

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