Question

The heat capacity at constant volume of a certain amount of a monatomic gas is 53.7 J/K.

(a) Find the number of moles of the gas. in mol

(b) What is the internal energy of the gas at T = 286 K? in kJ

(c) What is the heat capacity of the gas at constant pressure? in J/k

Answer 1

(a)

The heat capacity for one mole of monatomic gas is

C_V = 12.5 J/mol K

It is given that heat capacity at constant volume of a certain amount of a monatomic gas is

Q = 53.7 J/K

Now, the number of moles of the monatomic gas is

n = Q / C_V

    = 53.7 J/K / 12.5 J/mol K

= 4.296 mol

Rounding off to three significant figures, the number of moles of the monatomic gas is 4.30 mol.

(b)

The internal energy of the monatomic gas is

U = 3/2 nRT

Here, temperature is T and gas constant is R.

Substitute the values in the given equation,

U = 3/2 nRT

  = 3/2 (4.30 mol)(8.31 J / mol K)(286 K)

   =( 15329.5 J)(10^-3 kJ / 1 J)

= 15.3 kJ

Therefore, the internal energy of the gas is 15.3 kJ.

(c)

The heat capacity of the gas at constant pressure

C_P = C_V + nR

      = 53.7 J/K + (4.30 mol)( 8.31 J / mol K)

      = 89.433 J/K

Rounding off to three significant figures, the heat capacity of the gas at constant pressure is 89.4 J/K.