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Amit Saxena Grade: upto college level
`         A metal rod of cross-sectional area 1.0 cm2 is being heated at one end. At one time, the temperature gradient is 5.0°C/cm at cross-section A and is 2.5°C/cm at cross-section B. Calculate the rate at which the temperature is increasing in the part AB = 0.40 J/°C, thermal conductivity of the material of the rod = 200 W/m-°C. Neglect any loss of heat to the atmosphere.`
3 years ago

Navjyot Kalra
654 Points
```										Sol. The rate of heat flow per sec.
= dQ/dt = KA dθ/dt
The rate of heat flow per sec.
= dQ base A/dt = KA dθ base B/dt
This part of heat absorbed by the red.
Q/t = ms∆θ/dt where dθ/dt = Rate of net temp. variation
⇒ msdθ/dt = KA dθ base A/dt - KA dθ base B/dt ⇒ ms dθ/dt KA(dθ base A/dt - dθ base B/dt)
⇒ 0.4 * dθ/dt = 200 * 1 * 10^-4 (5 – 2.5) °C/cm
⇒ 0.4 * dθ/dt = 200 * 10^-4 * 2.5
⇒ 0.4 * dθ/dt = 200 * 2.5 * 10^-4/0.4 * 10^-2 °C/m = 1250 * 10^-2 = 12.5 °C/m

```
3 years ago
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