constant-volume calorimeter

Examples of constant-volume calorimeter in the following topics:

• Calorimetry

  • Constant-volume calorimetry is calorimetry performed at a constant volume.
  • This involves the use of a constant-volume calorimeter (one type is called a Bomb calorimeter).
  • For constant-volume calorimetry:
  • where δQ is the increment of heat gained by the sample, CV is the heat capacity at constant volume, cv is the specific heat at constant volume, and ΔT is the change in temperature.
  • Analyze the relationship between the gas constant for an ideal gas yield and volume

• 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.
  • To do so, the heat is exchanged with a calibrated object (calorimeter).
  • 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.
  • 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.

• 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.
  • A process in which a gas does work on its environment at constant pressure is called an isobaric process, while one in which volume is kept constant is called an isochoric process.
  • 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.
  • An isochoric process is one in which the volume is held constant, meaning that the work done by the system will be zero.

• Specific Heat for an Ideal Gas at Constant Pressure and Volume

  • An ideal gas has different specific heat capacities under constant volume or constant pressure conditions.
  • Specific Heat for an Ideal Gas at Constant Pressure and Volume
  • The heat capacity at constant volume of nR = 1 J·K−1 of any gas, including an ideal gas is:
  • where the partial derivatives are taken at: constant volume and constant number of particles, and at constant pressure and constant number of particles, respectively.
  • The heat capacity ratio or adiabatic index is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.

• Heat Capacity

  • Different measurements of heat capacity can therefore be performed, most commonly at constant pressure and constant volume.
  • Gases and liquids are typically also measured at constant volume.
  • This difference is particularly notable in gases where values under constant pressure are typically 30% to 66.7% greater than those at constant volume.
  • This defines the heat capacity at constant volume, CV.
  • Explain the enthalpy in a system with constant volume and pressure

• Constant Pressure

  • Isobaric processis a thermodynamic process in which the pressure stays constant (at constant pressure, work done by a gas is $P \Delta V$).
  • For an ideal gas, this means the volume of a gas is proportional to its temperature (historically, this is called Charles' law).
  • Because the change in volume of a cylinder is its cross-sectional area A times the displacement d, we see that Ad=ΔV, the change in volume.
  • Specific heat at constant pressure is defined by the following equation:
  • A graph of pressure versus volume for a constant-pressure, or isobaric process.

• Isothermal Processes

  • An isothermal process is a change of a thermodynamic system, in which the temperature remains constant.
  • For an ideal, the product of pressure and volume (PV) is a constant if the gas is kept at isothermal conditions.
  • The value of the constant is nRT, where n is the number of moles of gas present and R is the ideal gas constant.
  • For an isothermal, reversible process, this integral equals the area under the relevant pressure-volume isotherm, and is indicated in blue in for an ideal gas.
  • It is also worth noting that, for many systems, if the temperature is held constant, the internal energy of the system also is constant, and so $\Delta U = 0$.

• Human Metabolism

  • For example, one major factor in such activities is body temperature—normally kept constant by heat transfer to the surroundings, meaning that Q is negative (i.e., our body loses heat).
  • This energy is measured by burning food in a calorimeter, which is how the units are determined.
  • If you eat just the right amount of food, then your average internal energy remains constant.

• Volume Expansion

  • The subscript p indicates that the pressure is held constant during the expansion.
  • In the case of a gas, the fact that the pressure is held constant is important, as the volume of a gas will vary appreciably with pressure as well as with temperature.
  • where V is the volume of the material, and is dV/dT the rate of change of that volume with temperature.
  • The original volume will be V = L3,and the new volume, after a temperature increase, will be:
  • (c) Volume also increases, because all three dimensions increase.

• Equations of State

  • Boyle's law states that pressure P and volume V of a given mass of confined gas are inversely proportional:
  • while Charles' law states that volume of a gas is proportional to the absolute temperature T of the gas at constant pressure
  • where C is a constant which is directly proportional to the amount of gas, n (representing the number of moles).
  • The proportionality factor is the universal gas constant, R, i.e.
  • where k is Boltzmann's constant and N is the number of molecules.