The mathematical expression for heat capacity at constant pressure is given as:
[tex]Q=n\times C_{p}\times \Delta T[/tex] (1)
where, Q = heat capacity
[tex]C_{p}[/tex] = molar heat capacity at constant pressure
[tex]\Delta T[/tex] = change in temperature
n = number of moles
Therefore, [tex]\Delta T[/tex] = [tex]28.7^{o}C-21^{o}C[/tex]
= [tex]7.7 ^{o}C[/tex]
Number of moles =[tex]\frac{given mass in g}{molar mass}[/tex]
= [tex]\frac{14.6 g }{78.11 g/mol}[/tex]
= 0.186 mole
Put the values in formula (1)
[tex]330 J=0.186 mole\times C_{p}\times (7.7 ^{o}C+ 273) [/tex] (conversion of degree Celsius into kelvin)
[tex]C_{p} = \frac{330 J}{0.186 mole\times 280.7 K}[/tex]
= [tex]\frac{330 J}{52.2102 mole K}[/tex]
= 6.32 J /mol K
Hence, molar heat capacity of benzene at constant pressure = [tex]6.32 Jmol^{-1} K^{-1}[/tex]
