First Law Of Thermodynamics

First law of thermodynamics:

• When heat energy is given to a system then some part of heat energy supplied is used to change the internal energy of system and rest of energy is used to do external work.
• ∆Q=∆u+∆w

Note:

• For cyclic process, the change in internal energy of the system is zero because the system is brought back to the initial condition. Therefore, dU=0 and from the first law of thermodynamics,
• dQ= du + PdV =0+dW= dW

Molar Heat Capacities:

1) Molar heat capacity at constant pressure (Cp)

• Heat required to rise the temperature of one mole of gas through 1 degree C at constant pressure. Its unit is J/(molK)
• Heat required  (dQ)=n$C_p$ dT

2) Molar heat capacity at constant volume(Cv):

• Heat required to rise the temperature of mole of gas through 1 degree C at constant volume. Its unit is J/(molK)
• Heat required (dU) = n$C_v$dT

Mayer`s Formula:

• $C_p-C_v$=R

Specific heat capacities

1) Specific heat capacity at constant pressure ($c_p$):

• Heat required to rise the temperature of unit mass of gas through 1 degree C temperature at constant pressure.
• Heat required (dQ)=m $c_p$ dT
• $C_p$=M $c_p$

2) Specific heat capacity at constant volume ($c_v$):

• Heat required to rise the temperature of unit mass gas through 1 degree C temperature at constant volume.
• Its unit is J/(kg K)
• Heat required (du)=m $c_v$ dT
• $C_v$=M$c_v$ Hence, $c_p-c_v=\frac{R}{M}=r$

Note:

• Heat required to rise certain temperature at constant pressure is always greater than heat required to rise same temperature at constant volume. So gas has two types of heat capacities
• i.e. $C_p>C_v$
• Because in constant pressure, internal energy and work done both is done.