\(C_{P}=32\left(\frac{T}{400}\right)^{3}\)

\(Q=\int m \cdot c . d T=\int_{20}^{4} \frac{100}{1000} \times 32\left(\frac{T}{400}\right)^{3} d T\)

\(=\frac{32}{10} \times \frac{1}{(400)^{3}}\left(\frac{T^{4}}{4}\right)^{3}\)

\(=\frac{32}{10 \times(400)^{3}} \times \frac{1}{4}\left(20^{4}-4^{4}\right)\)

\(=\frac{32}{10 \times(400)^{3}} \times \frac{1}{4} \times(160000-256)\)

\(=0.002 W\)

\(\beta=\frac{T_{2}}{T_{1}-T_{2}}=\frac{Q_{3}}{W}\)

\(\Rightarrow \frac{20}{300-20}=\frac{0.2}{W} \Rightarrow W=0.028 kJ\)

\(\Rightarrow \frac{4}{300-4}=\frac{0.002}{W} \Rightarrow W=0.0148 kJ\)