Step 1: Understanding the Concept
Isochoric means constant volume, so \(\Delta V=0\) and the work \(W=P\Delta V=0\).
Step 2: First law
\(Q=\Delta U+W\) becomes \(Q=\Delta U\).
Step 3: The false statement
Heat added at constant volume raises the temperature, so \(\Delta T\) is generally not zero. \(\Delta T=0\) describes an isothermal process.
Final Answer:
The statement that Delta T equals zero is not true.
\[ \boxed{\text{(A) }\Delta T=0} \]