Why do price ceilings cause shortages? What is a black market and why might it alleviate shortages?

Price ceilings are something that is set in place by the government which limits the price of a certain good or service. So if a price ceiling is put into place it will most likely cause a shortage, because if gas costs $7.00 a gallon, and the government limits the price to only $1.75 a gallon people will want more gas. People will want more gas, because it is naturally cheaper and if gas is cheaper and people want the gas they will eventually run out of gas. A black market is where goods and services are sold illegally normally for a higher price. Black markets could alleviate shortages, because if all of the gas is gone and you can only buy it from the black market for say a price of $25 a gallon. So the black markets knows not as many people will buy gas for $25 a gallon vs. gas for $1.75 a gallon, so it makes for shortages to be relieved and harder for the black markets to go into a shortage.