Question

Need help deriving critical temperature for Bose condensation in 2D (see first reply for equations)

Answer 1

In class we derived the 3D case, but there's a step I don't understand:
\[N = g \cdot {V \over (2 \pi \hbar)^3} \cdot \int\limits_{0}^{\infty}{1 \over{e^{\left( E_p \over{K_B T}\right)}-1}} d^3 p\]
\[{} = g \cdot {V \over (2 \pi \hbar)^3} \cdot 4 \pi \cdot \int\limits_{0}^{\infty}{p^2 \over{e^{\left( E_p \over{K_B T}\right)}-1}} dp\]
... I feel like if I knew why that step made sense, I could figure out how to do the equivalent thing for the 2D case, but I'm stuck on that.