Which statement best explains why a hot-air balloon rises when the air in the balloon is heated?

a. According to Charles's law, the temperature of a gas is directly related to its volume. Thus the volume of the balloon increases, decreasing the density.

b. Hot air rises inside the balloon, and this lifts the balloon.

c. The temperature of a gas is directly related to its pressure. The pressure therefore increases, and this lifts the balloon.

d. Some of the gas escapes from the bottom of the balloon, thus decreasing the mass of gas in the balloon. This decreases the density of the gas in the balloon, and this lifts the balloon.

e. Temperature is related to the root mean square velocity of the gas molecules. Thus the molecules are moving faster, hitting the balloon more often, and thus lifting the balloon.

Justify your choice. For those you did not choose, explain why they are incorrect.