I'm confused about the third law of Thermodynamics.

The entropy of a perfect crystal at absolute zero is exactly equal to zero.

A consequence of third law is that

The heat capacity must go to zero at absolute zero

$${\displaystyle \lim _{T\rightarrow 0}C(T,X)=0.} $$

The law is also known in this way

In 1912 Nernst stated the law thus: "It is impossible for any procedure to lead to the isotherm $T = 0 $ in a finite number of steps."

I do not understand how $(1)$ agrees with the Nernst first statement.

We have $$Q=C \Delta T \implies \Delta T=Q/ C$$

So $C \to 0$ means that a small amount of heat exchanged causes a very large variation of temperature.

So why "it becomes difficult to lower a body's temperatue near $0K$"? Shouldn't it be easier instead ($C \to 0 \implies \Delta T \to \infty$)?

I'm confused about the third law of Thermodynamics.

The entropy of a perfect crystal at absolute zero is exactly equal to zero.

A consequence of third law is that

The heat capacity must go to zero at absolute zero

$$\displaystyle \lim _{T\rightarrow 0}C(T,X)=0 \tag{1}$$

The law is also known in this way

In 1912 Nernst stated the law thus: "It is impossible for any procedure to lead to the isotherm $T = 0 $ in a finite number of steps."

I do not understand how $(1)$ agrees with the Nernst first statement.

We have $$Q=C \Delta T \implies \Delta T=Q/ C$$

So $C \to 0$ means that a small amount of heat exchanged causes a very large variation of temperature.

So why "it becomes difficult to lower a body's temperatue near $0K$"? Shouldn't it be easier instead ($C \to 0 \implies \Delta T \to \infty$)?