Can we calculate the absolute value of entropy for an object for a particular state? As far as I previously knew, it is not possible to calculate the absolute magnitude of entropy.
$\Delta S=\frac{Q}{T}$
Entropy is defined as the heat added/released from the system divided by the temperature it was added/released at. So, it is impossible to measure absolute values for entropy since temperature changes as soon as any heat is added or released.
But in this video, Hank says that we can, in fact, measure absolute values for entropy. So, who is correct?
 A: 
Entropy is defined as the heat added/released from the system

Not quite. The infinitesimal (or differential) change in entropy is the reversibly(!) added heat $dS = Q/T$. To find the total change in entropy when the system is heated from $T_1\to T_2$, one must integrate this relation, i.e. add up all the infinitesimal changes $dS$.
Temperature is not the only quantity that defines the state the system is in. It is complemented by (at least) either pressure or (specific) volume. For the sake of specificity, let's assume the current state of the system is fully determined by temperature and pressure $(T,p)$.
Now, there are many ways the system could take to get from $T_1$ to $T_2$: the pressure might change in between, or it might not etc. That depends on the process under consideration.
And for each such process, the added/removed heat $\int Q$ could be different, even though the system starts and ends in the same state. Heat is not what is called a state function since it depends on the history of the system.
However, this changes when heat is divided by temperature.
Then, one ends up with a quantity (namely $dS$), that when integrated $\Delta S = \int Q/T$ is independent of the process, but only depends on the state at the start and at the end. I.e $\Delta S = S(T_2,p_2)-S(T_1,p_1)$. This is the entropy, and it is a state function.
To assign an absolute value to the entropy, one might pretend to heat the system up from absolute zero $T_1=0$, which is a natural reference point, because there entropy approaches a constant according to the third law of thermodynamics.
