Should the internal energy of a system necessarily increase if its tempreture is increased?

Should the internal energy of a system necessarily increase if heat is added to it?

The potential energy of a system increased if work is done

A cylinder containing a gas is lifted from the first floor to the second floor. What is the amount of work done on the gas? What is the amount of work done by the gas? Is the internal energy of the gas increased ? Is the tempreture of the gas increased?

The internal energy of the gas increases In

The internal energy of an ideal gas increases when it

Calculate the change in internal energy of 3 .0 mol of helium gas when its temperature is increased by 2. 0 K .

"When heat is added to a system, the internal energy of the system must increase". Justify this statement.