Step 1: Check statements A and B
Both say the internal energy changes, but the temperature is constant, so they are false.
Step 2: Check statement D
Heat is supplied, so $Q \gt 0$. With $\Delta U=0$, $W=Q \gt 0$, so the gas does positive work and D is false.
Step 3: Conclusion
Only statement C holds.
Final Answer:
Only the statement about unchanged internal energy is correct.
\[ \boxed{\text{(B) }\text{internal energy of the gas will not change}} \]