Final answer:
The change in internal energy of the gas in a rigid container receiving 1.70 x 10⁴ J of heat is equal to the amount of heat added, which is 1.70 x 10⁴ J.
Step-by-step explanation:
The question asks for the change in internal energy of an ideal gas that has received heat. According to the first law of thermodynamics, the change in internal energy of a system is equal to the heat added to the system minus the work done by the system on its surroundings.
If we have a rigid container, no work is done since the volume is constant and work (W) is a product of pressure and change in volume (W = P × ΔV), therefore the work done is zero. As such, the change in internal energy (U) is equal to the heat (Q) added to the system, which in this case is 1.70 x 10⁴ J.