  We show in this letter that the perturbed Burgers equation $u_t = 2uu_x +
u_{xx} + \epsilon ( 3 \alpha_1 u^2 u_x + 3\alpha_2 uu_{xx} + 3\alpha_3 u_x^2 +
\alpha_4 u_{xxx} )$ is equivalent, through a near-identity transformation and
up to order \epsilon, to a linearizable equation if the condition $3\alpha_1 -
3\alpha_3 - 3/2 \alpha_2 + 3/2 \alpha_4 = 0$ is satisfied. In the case this
condition is not fulfilled, a normal form for the equation under consideration
is given. Then, to illustrate our results, we make a linearizability analysis
of the equations governing the dynamics of a one-dimensional gas.
