Is the Specific Heat of a 1D Lattice Proportional to T/ΘD at Low Temperatures?

[poojagbn]

Homework Statement
Analyze the specific heat of a one dimensional lattice of identical atoms:
Show within Debye approximation that the specific heat at low temperatures ( ≪ Θ) is
proportional to T/Θ_D . Here Θ_D=ℏ_D/ k_B = ℏv_s/K_Ba is the Debye temperature valid for 1D, k_B the Boltzmann constant, a the lattice constant, v_s the velocity of sound and _D the Debye frequency.

The attempt at a solution
I know how to find out for a linear chain. But I do not know where to start in case of a 1-D lattice.

please help.

 

[PietKuip]

A 1D lattice is a chain.