1. Given relation between heat absorption rate and specific heat
   If the temperature is increased at a constant rate, then $\frac{dT}{dt}=\text{constant}$ Also, neglecting volume change, $\frac{dQ}{dt}=mC(T)\frac{dT}{dt}$ where $m$ is the mass of the solid.

So, since $m$ and $\dfrac{dT}{dt}$ are constant, $\frac{dQ}{dt}\propto C(T)$ Hence, the rate of heat absorption has the same variation with $T$ as the graph of specific heat capacity $C$ vs $T$.

2. Interpretation of the graph
   From the given standard shape:

• In the range $0$ to $100\,\text{K}$, $C$ increases approximately linearly with $T$.
• In the range $200$ to $300\,\text{K}$, $C$ increases.
• In the range $400$ to $500\,\text{K}$, $C$ is approximately constant.
• Heat absorbed over a temperature interval is $Q=m\int C(T)\,dT$ so it is proportional to the area under the $C$ vs $T$ graph over that interval.

3. Check Option A
   In $0$-$100\,\text{K}$, since $C$ varies linearly with $T$ approximately, and $\frac{dQ}{dt}\propto C(T),$ the rate of heat absorption also varies linearly with $T$.

So, A is correct.

4. Check Option B
   Heat absorbed from $0$ to $100\,\text{K}$: $Q_{0\to100}=m\int_0^{100} C(T)\,dT$ This is the area under the graph in the low-temperature region, which is small because $C$ is small there.

Heat absorbed from $400$ to $500\,\text{K}$: $Q_{400\to500}=m\int_{400}^{500} C(T)\,dT$ Here $C$ is large and nearly constant, so the area is much larger.

Thus, $Q_{0\to100}<Q_{400\to500}$ So, B is correct.

5. Check Option C
   In the range $400$-$500\,\text{K}$, the graph shows $C$ approximately constant. Since $\frac{dQ}{dt}=mC\frac{dT}{dt},$ and both $C$ and $\dfrac{dT}{dt}$ are constant in this range, the rate of heat absorption remains constant.

So, C is correct.

6. Check Option D
   In the range $200$-$300\,\text{K}$, the graph shows $C$ increasing with $T$. Therefore, $\frac{dQ}{dt}\propto C(T)$ so the rate of heat absorption also increases in this interval.

So, D is correct.

7. Final answer
   All four statements are correct: $\boxed{A,\ B,\ C,\ D}$

8. Comparison with stored correct answer
   Stored correct answer: $A, B, C, D$
   Derived answer: $A, B, C, D$

They match exactly.