constant-pressure calorimeter

Examples of constant-pressure calorimeter in the following topics:

• Constant-Pressure Calorimetry

  • A constant-pressure calorimeter measures the change in enthalpy of a reaction at constant pressure.
  • A constant-pressure calorimeter measures the change in enthalpy of a reaction occurring in a liquid solution.
  • In that case, the gaseous pressure above the solution remains constant, and we say that the reaction is occurring under conditions of constant pressure.
  • A simple example of a constant-pressure calorimeter is a coffee-cup calorimeter, which is constructed from two nested Styrofoam cups and a lid with two holes, which allows for the insertion of a thermometer and a stirring rod.
  • A styrofoam cup with an inserted thermometer can be used as a calorimeter, in order to measure the change in enthalpy/heat of reaction at constant pressure.

• Calorimetry

  • This involves the use of a constant-volume calorimeter (one type is called a Bomb calorimeter).
  • A constant-pressure calorimeter measures the change in enthalpy of a reaction occurring in solution during which the atmospheric pressure remains constant.
  • where Cp is the specific heat at constant pressure, ΔH is the enthalpy of the solution, ΔT is the change in temperature, W is the mass of the solute, and M is the molecular mass of the solute.
  • The measurement of heat using a simple calorimeter, like the coffee cup calorimeter, is an example of constant-pressure calorimetry, since the pressure (atmospheric pressure) remains constant during the process.
  • Constant-pressure calorimetry is used in determining the changes in enthalpy occurring in solution.

• Constant-Volume Calorimetry

  • Constant-volume calorimeters, such as bomb calorimeters, are used to measure the heat of combustion of a reaction.
  • A bomb calorimeter is a type of constant-volume calorimeter used to measure a particular reaction's heat of combustion.
  • As such, bomb calorimeters are built to withstand the large pressures produced from the gaseous products in these combustion reactions.
  • Since the volume is constant for a bomb calorimeter, there is no pressure-volume work.
  • Thus, the total heat given off by the reaction is related to the change in internal energy (ΔU), not the change in enthalpy (ΔH) which is measured under conditions of constant pressure.

• Solving Problems with Calorimetry

  • They range from simple coffee cup calorimeters used by introductory chemistry students to sophisticated bomb calorimeters used to determine the energy content of food.
  • A different type of calorimeter that operates at constant volume, colloquially known as a bomb calorimeter, is used to measure the energy produced by reactions that yield large amounts of heat and gaseous products, such as combustion reactions.
  • The sample is placed in the bomb, which is then filled with oxygen at high pressure.
  • Bomb calorimeters require calibration to determine the heat capacity of the calorimeter and ensure accurate results.
  • This is the picture of a typical setup of bomb calorimeter.

• Gauge Pressure and Atmospheric Pressure

  • Pressure is often measured as gauge pressure, which is defined as the absolute pressure minus the atmospheric pressure.
  • In most measurements and calculations, the atmospheric pressure is considered to be constant at 1 atm or 101,325 Pa, which is the atmospheric pressure under standard conditions at sea level.
  • In this equation p0 is the pressure at sea level (101,325 Pa), g is the acceleration due to gravity, M is the mass of a single molecule of air, R is the universal gas constant, T0 is the standard temperature at sea level, and h is the height relative to sea level.
  • Gauge pressure is a relative pressure measurement which measures pressure relative to atmospheric pressure and is defined as the absolute pressure minus the atmospheric pressure.
  • For example, tire pressure and blood pressure are gauge pressures by convention, while atmospheric pressures, deep vacuum pressures, and altimeter pressures must be absolute.

• Constant Pressure and Volume

  • Isobaric process is one in which a gas does work at constant pressure, while an isochoric process is one in which volume is kept constant.
  • An isobaric process occurs at constant pressure.
  • Since the pressure is constant, the force exerted is constant and the work done is given as PΔV.
  • If a gas is to expand at a constant pressure, heat should be transferred into the system at a certain rate.
  • Since pressure is constant, the work done is PΔV.

• Pressure and Free Energy

  • Gibbs free energy measures the useful work obtainable from a thermodynamic system at a constant temperature and pressure.
  • When a system changes from an initial state to a final state, the Gibbs free energy (ΔG) equals the work exchanged by the system with its surroundings, minus the work of the pressure force.
  • Gibbs energy (also referred to as ∆G) is also the chemical potential that is minimized when a system reaches equilibrium at constant pressure and temperature.
  • As such, it is a convenient criterion of spontaneity for processes with constant pressure and temperature.
  • Therefore, Gibbs free energy is most useful for thermochemical processes at constant temperature and pressure.

• Expressing the Equilibrium Constant of a Gas in Terms of Pressure

  • For gas-phase reactions, the equilibrium constant can be expressed in terms of partial pressures, and is given the designation KP.
  • For gas-specific reactions, however, we can also express the equilibrium constant in terms of the partial pressures of the gases involved.
  • Our equilibrium constant in terms of partial pressures, designated KP, is given as:
  • Note that in order for K to be constant, temperature must be constant as well.
  • Therefore, the term RT is a constant in the above expression.

• Constant Pressure

  • Isobaric processis a thermodynamic process in which the pressure stays constant (at constant pressure, work done by a gas is $P \Delta V$).
  • An isobaric process is a thermodynamic process in which pressure stays constant: ΔP = 0.
  • Since the pressure is constant, the force exerted is constant and the work done is given as W=Fd, where F (=PA) is the force on the piston applied by the pressure and d is the displacement of the piston.
  • Specific heat at constant pressure is defined by the following equation:
  • A graph of pressure versus volume for a constant-pressure, or isobaric process.

• Variation of Pressure With Depth

  • For any given liquid with constant density throughout, pressure increases with increasing depth.
  • For many liquids, the density can be assumed to be nearly constant throughout the volume of the liquid and, for virtually all practical applications, so can the acceleration due to gravity (g = 9.81 m/s2).
  • Equation 2 by itself gives the pressure exerted by a liquid relative to atmospheric pressure, yet if the absolute pressure is desired, the atmospheric pressure must then be added to the pressure exerted by the liquid alone.
  • Thus the force contributing to the pressure of a gas within the medium is not a continuous distribution as for liquids and the barometric equation given in must be utilized to determine the pressure exerted by the gas at a certain depth (or height) within the gas (p0 is the pressure at h = 0, M is the mass of a single molecule of gas, g is the acceleration due to gravity, k is the Boltzmann constant, T is the temperature of the gas, and h is the height or depth within the gas).
  • The force contributing to the pressure of a gas within the medium is not a continuous distribution as for liquids and the barometric equation given in this figure must be utilized to determine the pressure exerted by the gas at a certain depth (or height) within the gas (p0 is the pressure at h = 0, M is the mass of a single molecule of gas, g is the acceleration due to gravity, k is the Boltzmann constant, T is the temperature of the gas, and h is the height or depth within the gas)