$R$~~$8\mathrm{.}31J*K^{-1}*mo{l}^{-1}$

$k_B$~~$1\mathrm{.}38{10}^{-23}J*K^{-1}$

$N_A$~~$6\mathrm{.}02{10}^{23}mo{l}^{-1}$

A sealed box has a volume of $5$ liters. Assume it contains $2$ moles of ideal gas at a temperature of $27C.$

a$)$ How many gas molecules are there in the box?

b$)$ What is the pressure of the gas?

c$)$ Without changing the box, the gas inside is slowly heated up to $77C.$ What is the pressure of the gas now?

d$)$ With the temperature maintained at $77C,$ the box is slowly expanded to twice its original volume. What is the pressure of the gas now?