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Molar heat capacity: Difference between revisions

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Adding heat to a substance changes its temperature in accordance to <cmath>\Delta Q=nc_M\Delta T</cmath>
Adding heat to a substance changes its temperature in accordance to <cmath>\Delta Q=nc_M\Delta T</cmath>
<math>\Delta Q=</math> change in heat
<math>\Delta Q=</math> change in heat
<br />
<math>n=</math> moles of substance
<math>n=</math> moles of substance
<br />
<math>c_M=</math> molar heat capacity
<math>c_M=</math> molar heat capacity
<br />
<math>\Delta T=</math> change in temperature
<math>\Delta T=</math> change in temperature
 
<br />
<br />
At constant volume, <math>c_M=c_V</math>.
At constant volume, <math>c_M=c_V</math>.
<br />
At constant pressure, <math>c_M=c_P</math>.
At constant pressure, <math>c_M=c_P</math>.
 
<br />
For an ideal gas, <math>c_P=c_V+R</math>.
<br />
For an ideal gas, <math>c_P=c_V+R</math> where <math>R=</math> the ideal gas constant.
<br />
For an incompressible substance, <math>c_P=c_V</math>.
For an incompressible substance, <math>c_P=c_V</math>.
 
<br />
<br />
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>.

Revision as of 04:30, 27 November 2019

Adding heat to a substance changes its temperature in accordance to \[\Delta Q=nc_M\Delta T\] $\Delta Q=$ change in heat
$n=$ moles of substance
$c_M=$ molar heat capacity
$\Delta T=$ change in temperature

At constant volume, $c_M=c_V$.
At constant pressure, $c_M=c_P$.

For an ideal gas, $c_P=c_V+R$ where $R=$ the ideal gas constant.
For an incompressible substance, $c_P=c_V$.

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

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