Question

E28.12.) When 229 ) of energy is supplied as heat at constant pressure to 3.0 mol Ar(g) the temperature of the sample increases by 2.55 K. Calculate the molar heat capacities at constant volume and constant pressure of the gas.

Answer 1

Answer : The molar heat capacity at constant volume and constant pressure is 29.9 J/mol.K and 38.2 J/mol.K respectively.

Explanation :

Formula used for specific heat at constant volume :

$q_v=n\times c_v\times \Delta T$

where,

$q_v$ = heat = 229 J

n = moles of gas = 3.0 mol

$c_v$ = molar heat capacity at constant volume = ?

$\Delta T$ = change in temperature  = 2.55 K

Now put all the given value in the above formula, we get:

$229J=3.0mol\times c_v\times 2.55K$

$c_v=29.9J/mol.K$

The molar heat capacity at constant volume is 29.9 J/mol.K

Now we have to calculate the molar heat capacity at constant pressure.

Formula used :

$c_p-c_v=R$

where,

$c_v$ = molar heat capacity at constant volume = 29.9 J/mol.K

$c_p$ = molar heat capacity at constant pressure = ?

R = gas constant = 8.314 J/mol.K

Now put all the given value in the above formula, we get:

$c_p-29.9J/mol.K=8.314J/mol.K$

$c_p=38.2J/mol.K$

The molar heat capacity at constant pressure is 38.2 J/mol.K