Pleasw SOLVE USING SIMULINKAssume that there is no heat exchange between a bath and the surroundings but that the

bath temperature can change due to heat released from a pellet that is put in the bath.

Now both the pellet temperature $T(t)$ and the bath temperature $T_f(t)$ will vary with time.

Take the initial pellet and bath temperatures to be $100C$ and $20C$ respectively, the

mass $m,$ surface area A and heat capacity $C$ of the pellet to be $0\mathrm{.}02kg,0\mathrm{.}001m^2$ and $800$

$\frac{J}{k}gC,$ and the heat transfer coefficient $h$ to be $200\frac{J}{s}{m}^{2}C.$ The mass $m_f$ and heat

capacity $C_f$ of the bath are $0\mathrm{.}1kg$ and $4000\frac{J}{k}gC.$ The energy balance for the pellet is:

$d\frac{T}{d}t=-(h\frac{A}{M}C)(T-T_f),T(0)=100C$

And for the bath:

$d\frac{T_f}{d}t=(h\frac{A}{M_f}{C}_f)(T-T_f),T_f(0)=20C$

Simulate this system using SIMULINK. Plot $T$ and $T_f$ versus time on the same graph.

What is the final equilibrium temperature of the system? Submit your block diagram,

the scope showing the results and your answer for the final equilibrium

temperature.

Now run one more case. Change the mass of the bath fluid from $0\mathrm{.}1kg$ to $10kg.$

Submit the resulting scope and comment on how this result is different from the

first case.