# Difference between revisions of "Molar heat capacity"

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− | + | The molar heat capacity is the amount of energy required to change the temperature of an amount of substance by a certain amount per moles of the substance and change in temperature. | |

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− | + | Adding [[heat]] to a substance changes its temperature in accordance to <cmath>\Delta Q=nc_M\Delta T,</cmath> | |

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− | For an ideal gas, <math>c_P=c_V+R</math>. | + | where |

− | For an incompressible substance, <math>c_P=c_V</math>. | + | <math>\Delta Q</math> is the change in heat, <math>n</math> is the number of moles of substance, <math>c_M</math> is the molar heat capacity, and |

+ | <math>\Delta T</math> is the change in temperature. | ||

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+ | At constant volume, <math>c_M=c_V</math>. At constant pressure, <math>c_M=c_P</math>. | ||

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+ | For an ideal gas, <math>c_P=c_V+R</math> where <math>R=</math> the ideal gas constant. For an incompressible substance, <math>c_P=c_V</math>. | ||

In adiabatic compression (<math>\Delta Q=0</math>) of an ideal gas, <math>PV^\gamma</math> stays constant, where <math>\gamma=\frac{c_V+R}{c_V}</math>. | In adiabatic compression (<math>\Delta Q=0</math>) of an ideal gas, <math>PV^\gamma</math> stays constant, where <math>\gamma=\frac{c_V+R}{c_V}</math>. | ||

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+ | == See Also == | ||

+ | *An excellent derivation of the last equation can be found [https://www.animations.physics.unsw.edu.au/jw/Adiabatic-expansion-compression.htm here]. | ||

+ | * [[Heat]] | ||

+ | * [[Thermodynamics]] | ||

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+ | [[Category: Physics]] | ||

+ | {{stub}} |

## Latest revision as of 12:02, 1 August 2020

The molar heat capacity is the amount of energy required to change the temperature of an amount of substance by a certain amount per moles of the substance and change in temperature.

Adding heat to a substance changes its temperature in accordance to

where is the change in heat, is the number of moles of substance, is the molar heat capacity, and is the change in temperature.

At constant volume, . At constant pressure, .

For an ideal gas, where the ideal gas constant. For an incompressible substance, .

In adiabatic compression () of an ideal gas, stays constant, where .

## See Also

- An excellent derivation of the last equation can be found here.
- Heat
- Thermodynamics

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