A gas is enclosed in a cylinder with a weightless, frictionless piston open to the atmosphere ($1.0\mathrm{atm}$). Which statements are correct?

1. AThe pressure of the gas stays at $1.0\mathrm{atm}$ whatever the temperature
2. BHeating the gas from $300\mathrm{K}$ to $450\mathrm{K}$ increases its volume by $50\%$
3. CThe density of the gas is inversely proportional to its kelvin temperature
4. DIf the piston is clamped and the gas is heated from $300$ to $450\mathrm{K}$, the pressure becomes $1.5\mathrm{atm}$