Respuesta :
Answer : The value of [tex]c_p[/tex] for reversible and adiabatic expansion is 55.04 J/mol.K
Explanation : Given,
Temperature at equilibrium = [tex]T_1=25^oC=273+25=298K[/tex]
Pressure at equilibrium = [tex]P_1=121.3kPa[/tex]
Temperature at adiabatic reversible expansion = [tex]T_2[/tex]
Pressure at adiabatic reversible expansion = [tex]P_2=101.3kPa[/tex]
Temperature at constant volume process = [tex]T_3=25^oC=273+25=298K[/tex]
Pressure at constant volume process = [tex]P_3=104.0kPa[/tex]
First we have to calculate the temperature at adiabatic reversible expansion.
Gay-Lussac's Law : It is defined as the pressure of the gas is directly proportional to the temperature of the gas at constant volume and number of moles.
[tex]P\propto T[/tex]
or,
[tex]\frac{P_2}{T_2}=\frac{P_3}{T_3}[/tex]
Now put all the given values in the above equation, we get:
[tex]\frac{101.3kPa}{T_2}=\frac{104.0kPa}{298K}[/tex]
[tex]T_2=290K[/tex]
Now we have to calculate the value of [tex]c_p[/tex] for reversible and adiabatic.
Formula used :
[tex]T_2=T_1(\frac{P_2}{P_1})^{\frac{R}{c_p}}[/tex]
Now put all the given values in the above equation, we get:
[tex]290=298\times (\frac{101.3}{121.3})^{\frac{8.314}{c_p}}[/tex]
[tex]c_p=55.04J/mol.K[/tex]
Therefore, the value of [tex]c_p[/tex] for reversible and adiabatic expansion is 55.04 J/mol.K
