Name: ideal gas heat capacity at constant pressure
Uploaded: 2023-04-30T12:32:05.000Z
Duration: 1 min 14 s
Channel: JoVE

K12 Standards

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New York State Science Learning Standards

High School

Physical Science

HS. Energy

HS-PS3-3.

Heat Capacities of an Ideal Gas I

Consider two identical cylinders A and B, filled with an ideal gas. Cylinder A is sealed, while B has a movable piston.
Let some amount of heat be applied to both cylinders to increase the gas temperature equally.
The volume of gas in the enclosed cylinder remains unchanged, so no work is done. In cylinder B, the gas is free to expand, resulting in some work being done under constant external pressure.
From the First law of thermodynamics, the heat applied increases the system&#39;s internal energy in cylinder A.&#160; In cylinder B, a portion of heat is used to do work.
As the temperature is the same in both the cylinders, their internal energy change is also the same.
Since more heat should be added to cylinder B than A to raise their temperature equally, two distinct molar heat capacities are defined.
CV and Cp are the amounts of heat needed to raise the temperature of one mole of gas by 1 unit under constant volume and pressure, respectively.

heat capacities of an ideal gas i

Heat capacity is the ratio of heat absorbed by the substance corresponding to its temperature change. It is also called thermal capacity and the SI unit of heat capacity is J/K. Whereas, specific heat capacity is defined as the amount of heat necessary to change the temperature of 1 kg of a substance by 1 K and is also called massic heat capacity. Its SI unit is J/kg&#8901;K.
Molar heat capacity quantifies the ratio of the amount of heat added (or removed) to increase (or decrease) the temperature of 1 mole of a substance by 1 K, either measured under a constant volume or constant pressure. Molar heat capacity is one of the characteristics of a substance and is also called molar specific heat. Its SI unit is J/mol&#183;K. Measuring the molar heat capacity at constant volume is the easiest. The system acquires infinite number of possible heat capacities if neither the pressure nor the volume is constant. In most cases, the molar heat capacity at constant pressure (CP) is higher than the molar heat capacity at constant volume (CV). For example, the air has 40% greater CP than CV.

Heat capacity is the ratio of heat absorbed by the substance corresponding to its temperature change. It is also called thermal capacity and the SI unit ...

Education

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Physics

Unit 1

The First Law of Thermodynamics

KEY TERMS AND CONCEPTS

ideal gas heat capacity at constant pressure

Heat capacity describes how much heat a substance absorbs for a given change in temperature. It is also called thermal capacity, and its SI unit is J/K. Specific heat capacity is the heat needed to raise the temperature of 1 kg of a substance by 1 K, and its SI unit is J/kg·K.

The video also explains molar heat capacity. This is the amount of heat added or removed to change the temperature of 1 mole of a substance by 1 K. It can be measured at constant volume or constant pressure, and it is also called molar specific heat. Its SI unit is J/mol·K.

For ideal gases, measuring the molar heat capacity at constant volume is the easiest. If neither pressure nor volume stays constant, the system can have infinitely many possible heat capacities. In many cases, the molar heat capacity at constant pressure, C P, is higher than the molar heat capacity at constant volume, C V. For air, C P is about 40% greater than C V.

Ideal Gas Heat Capacity at Constant Pressure

ideal-gas-heat-capacity-at-constant-pressure

thermodynamic systems

Open, Closed, and Isolated Systems

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first law of thermodynamics: problem-solving

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Isothermal Expansion and Heat Transfer

An isothermal process is a thermodynamic process that happens at constant temperature. During the process, heat slowly flows into the system or out of the system so thermal equilibrium is maintained. Phase changes are common examples of isothermal processes. Water can evaporate into steam at a constant temperature, and water can also freeze into ice at a constant temperature. An ideal gas can also undergo isothermal expansion or compression. Here, an ideal gas in an isolated cylinder expands...

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Constant Volume and Pressure in Thermodynamics

Thermodynamic processes can happen at constant volume or at constant pressure. An isochoric process is a constant-volume process. In this case, the volume does not change, so the work done by the system is zero. The first law of thermodynamics still applies, so any heat added or removed changes the internal energy of the system only. A simple example is heating 1000 g of water from 40 degrees celsius to 70 degrees celsius at constant volume. Because the process is isochoric, no work is done by...

Heat capacity describes how much heat a substance absorbs for a given change in temperature. It is also called thermal capacity, and its SI unit is J/K. Specific heat capacity is the heat needed to raise the temperature of 1 kg of a substance by 1 K, and its SI unit is J/kg·K. The video also explains molar heat capacity. This is the amount of heat added or removed to change the temperature of 1 mole of a substance by 1 K. It can be measured at constant volume or constant pressure, and it is...

heat capacities of an ideal gas ii

Ideal Gas Heat Capacity Differences

Ideal gas heat capacities depend on whether the gas is heated at constant volume or constant pressure. At constant volume, the heat absorbed only raises the internal energy of the system. No work is done in this case. At constant pressure, the situation is different. The heat absorbed increases the internal energy and also does work. Molar heat capacity is the heat needed to raise the temperature of 1 mole of gas by 1 unit. Because some of the added heat goes into work, more heat is needed at...

heat capacities of an ideal gas iii

Ideal Gas Heat Capacity and Degrees of Freedom

Ideal gas heat capacity depends on degrees of freedom, which are the independent ways a gas molecule can move, rotate, and vibrate. If d is the number of degrees of freedom, the molar heat capacity at constant volume can be written in terms of d. The molar heat capacity at constant pressure can also be written using the relationship between the two heat capacities. The ratio of molar heat capacity at constant pressure to molar heat capacity at constant volume is called the ratio of heat...

adiabatic processes for an ideal gas

Gas Temperature Changes in Adiabatic Processes

Adiabatic processes change the temperature of an ideal gas without heat transfer. In an adiabatic compression, no heat is added, but work is done on the gas. That work raises the gas temperature. In an adiabatic expansion, the gas does work and its temperature drops. A common example is the compression of a gas-air mixture inside a car engine cylinder. The compression happens so quickly that there is no time for heat to move between the mixture and its surroundings. Even so, the work done on...

pressure and volume in an adiabatic process

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Free Expansion: Pressure, Volume, and Temperature

Free expansion shows how pressure, volume, and temperature behave when a gas expands without doing work. It is an adiabatic process, but it is not the same as adiabatic expansion. In free expansion, no work is done and the internal energy does not change. In adiabatic expansion, work is done and the internal energy changes. For an adiabatic process, the pressure-volume relation comes from the adiabatic condition. That relation does not apply to free expansion, even though the expansion is...

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Adiabatic Compression in an Engine Cylinder

Adiabatic compression in an engine cylinder changes the pressure, temperature, and volume of a gas-air mixture. In this setup, gasoline vapor is injected into the cylinder when the piston is in its expanded position. The mixture starts at 20 °C, 1.00 x 10^5 N/m^2, and 240 cm^3. The mixture is then compressed adiabatically to 40 cm^3. Adiabatic means no heat is exchanged with the surroundings during the process. For this calculation, the compression is treated as quasi-static, even though real...

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Energy Forms in Thermodynamics

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Maxwell's thermodynamic relations help solve problems in thermodynamics. They connect partial differentials for quantities that are hard to measure in the lab with quantities that are easier to measure. This makes them useful for working with temperature, pressure, volume, and entropy. These relations come from thermodynamic potentials and the symmetry of second derivatives. Thermodynamic potentials are exact differentials, so the order of second differentiation does not change the result.

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Gas Cooling and Heating in Throttling

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key terms and concepts

Learn heat capacity, specific heat capacity, and molar heat capacity for ideal gases, including the difference between constant pressure and constant volume.

Ideal Gas Heat Capacity at Constant Pressure | JoVE K12

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HS-PS3-4.

Ideal Gas Heat Capacity at Constant Pressure

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