There is a tonk of $5000L$ total volume. The tank initially contains $1000L$ of a liquid at $90C$ is feeding the tank, whle $100\frac{L}{m}in$ of liquid is discherging prom the tonk at a temperature $(T)C.$ When the inlet and outlet volves ore opened, on exotherm $C$ recoction tokes place within the fluid in the tank, and $400$kjlmin of energy is thas generated. At the same time, heat is lost to the ombient ar $30C$ with $A=2m^2$ and $h=20\frac{W}{m^2}K.$ Assming constant density $(1k\frac{g}{L})$ and constont cp$(4$kj $(\frac{\text{:}}{k}gC\}$ and perfect mixing. Which rquation shows the volume of the liquid in the tonk os a function of time?

a$)V=100t+1000$

b$)V=1000L$ and it is consiont

c$)V=100t-1000$

d$)V=100t+4000$

Derive the equation for temperature of liquid in the tonk as a function of time.

a$)82\mathrm{.}5-41\mathrm{.}66(1+0\mathrm{.}06t{)}^{-2\mathrm{.}04}$

b$)82\mathrm{.}5+41\mathrm{.}66(1+0\mathrm{.}06t{)}^{-2\mathrm{.}04}$

c$)37\mathrm{.}6+16\mathrm{.}66(0\mathrm{.}1t-1{)}^{-0\mathrm{.}5}$

d$)37\mathrm{.}6-16\mathrm{.}66(0\mathrm{.}1t+1{)}^{-0\mathrm{.}5}$

Calculote the temperature $(C)$ of the liquid in the tank after $30$min.

a$)28\mathrm{.}33$

b$)77\mathrm{.}40$

c$)20\mathrm{.}00$

d$)81\mathrm{.}40$

Calculote the temperoture $(C)$ when tonk is full $(V=5000L)$

a$)20\mathrm{.}00$

b$)77\mathrm{.}40$

c$)36\mathrm{.}71$

d$)25\mathrm{.}55$