Examples of constant-pressure calorimeter in the following topics:
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- 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.
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- 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.
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- 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.
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- 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.
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- 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.
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- 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)
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- 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 pressure of 1 J·K−1 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.
- It is a simple equation relating the heat capacities under constant temperature and under constant pressure.
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- Bernoulli's equation states that for an incompressible and inviscid fluid, the total mechanical energy of the fluid is constant .
- The SI unit of static pressure and dynamic pressure is the pascal.
- Static pressure is simply the pressure at a given point in the fluid, dynamic pressure is the kinetic energy per unit volume of a fluid particle.
- Therefore, if there is no change in potential energy along a streamline, Bernoulli's equation implies that the total energy along that streamline is constant and is a balance between static and dynamic pressure.
- Given that any energy exchanges result from conservative forces, the total energy along a streamline is constant and is simply swapped between potential and kinetic.
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- In practice, pressure is most often measured in terms of gauge pressure.
- Gauge pressure is the pressure of a system above atmospheric pressure.
- Since atmospheric pressure is mostly constant with little variation near sea level, where most practical pressure measurements are taken, it is assumed to be approximately 101,325 Pa.
- Gauge pressure is much more convenient than absolute pressure for practical measurements and is widely used as an established measure of pressure.
- Many modern pressure measuring devices are pre-engineered to output gauge pressure measurements.
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- Pressure in a Tire - Assuming that the air molecules inside a car tire behave like an ideal gas and that the volume of the tire is constant, find the additional number of molecules, nΔ, that must be added to the tire at the coldest temperature, Tmin, of the year so as to achieve the same tire pressure, P0, that is achieved at the hottest temperature, Tmax, of the year, in terms of the number of molecule, nmax, that are required at Tmax to achieve P0.
- The elementary mathematical expression for pressure is given by:
- Finally, when considering a given force of constant magnitude acting on a constant area of a given surface, the pressure exerted by that force on that surface will be greater the larger the angle of that force as it acts upon the surface, reaching a maximum when that force acts perpendicular to the surface.
- where n is the number of gas molecules, R is the ideal gas constant (R = 8.314 J mol-1 K-1), T is the temperature of the gas, and V is the volume of the container.
- Another common type of pressure is that exerted by a static liquid or hydrostatic pressure.