Question

What is the increase in entropy if 14 mol of N_2 are heated from
20.0◦C to 30.0◦C at constant pressure, assuming nitrogen behaves as
an ideal gas?
(b) A kettle holds 1.50 kg of water. Calculate the internal energy
increase of the water as its temperature increases from 20.0◦C to
90.0◦C. The specific heat capacity of water is 4.18 kJ kg
−1.

Answer 1

a) Formula for change in entropy is,

ΔS = Cp * ln (T2/T1)

For ideal diatomic gas, degree of freedom is 5

Then we have ,

Cp= (1+ f/2)R

i.e. Cp = 7/2 R, where R is gas constant having value 8.314 per mol per kelvin

T2= 273+30= 303K and T1= 273+20= 293K

So, by the formula

ΔS= 14 * 3.5 * 8.314 * ln (303/293)

ΔS= 14 * 3.5 * 8.314 * 0.033

ΔS= 13.44J/K

b) The formula for increase in internal energy is given by,

ΔU= mCv dT

ΔU= mCv(T2 - T1)

ΔU= 1.5 * 4.18 * ( 363-293)

ΔU= 1.5 * 4.18 * 70

ΔU= 438.9