Question

A hollow cylindrical pipe of length $10\text{cm}$ has inner radius $r_1=3\text{cm}$ and outer radius $r_2=12\text{cm}$. The temperature difference between the inner and outer layer of cylindrical pipe is ${100}^{\circ }\text{C}$ and the thermal conductivity of cylindrical pipe is $150{\text{W/m}}^{\circ }\text{C}$. Find the rate of heat transfered (in $\text{kW}$) between inner and outer layers.
(Take $\ln 2=0.693$)

• A. $3.4$
• B. $6.8$
• C. $10$
• D. $13.6$

Answer 1

The correct option is B $6.8$

Given,
Length of the cylindrical pipe $\left(l\right)=10\text{cm}=0.1\text{m}$
Inner radius of cylindrical pipe $\left(r_1\right)=3\text{cm}$
Outer radius of cylindrical pipe $\left(r_2\right)=12\text{cm}$
Temperature difference $\left(\Delta T\right)={100}^{\circ }\text{C}$
Thermal conductivity $\left(k\right)=150{\text{W/m}}^{\circ }\text{C}$
Then,
Rate of heat transfer $\left(H\right)=\frac{2\pi lk\Delta T}{\ln \left(\frac{r_2}{r_1}\right)}$
$=\frac{2\times 3.14\times 0.1\times 150\times 100}{\ln \left(\frac{12}{3}\right)}$
$=6.8\text{kW}$