Difference between revisions of "Molar heat capacity"
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| − | Adding heat to a substance changes its temperature in accordance to <cmath>\Delta Q=nc_M\Delta T</cmath> | + | 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. |
| − | <math>\Delta Q | + | |
| − | + | Adding [[heat]] to a substance changes its temperature in accordance to <cmath>\Delta Q=nc_M\Delta T,</cmath> | |
| − | <math>n | + | |
| − | + | where | |
| − | <math>c_M | + | <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. | |
| − | <math>\Delta T | + | |
| − | + | At constant volume, <math>c_M=c_V</math>. At constant pressure, <math>c_M=c_P</math>. | |
| − | + | ||
| − | At constant volume, <math>c_M=c_V</math>. | + | 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>. |
| − | + | ||
| − | At constant pressure, <math>c_M=c_P</math>. | ||
| − | |||
| − | |||
| − | 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>. | ||
| + | |||
| + | == 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]] | ||
| + | |||
| + | |||
| + | [[Category: Physics]] | ||
| + | {{stub}} | ||
Latest revision as of 11:02, 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 ![\[\Delta Q=nc_M\Delta T,\]](http://latex.artofproblemsolving.com/1/3/a/13a7fd6bf5581fdc8e7807b49fb2bfc822c3bfc6.png)
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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