Direction: Heat is being transferred by convection from water at 48°C to a glass plate whose surface temp. is exposed to the water is at 40°C. The thermal conductivity of water is 0.6 W/mK and the thermal conductivity of glass is 1.2 W/mK. The spatial gradient of temperature in the water at the water-glass interface is dT/dy = 1 × 104 K/m.
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The value of the temperature gradient in the glass at the water-glass interface in K/m is
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- –2 × 104
- 0.0
- 0.5 × 104
- 2 × 104
- –2 × 104
Correct Option: C
Temperature of water = 48° C
Temperature of glass plate = 40° C
Thermal conductivity of water = kw = 0.6 W/mK Thermal conductivity of glass = kG = 1.2 W/mK
The spatial gradient of temperature in water at the water-glass interface
| = |  |  | = 1 × 105 K/m | |
| dy |
At water glass interface
| q = kw | | | = kG | | | ||||
| dy | w | dy | G |
| ⇒ | | | = | × | | | |||||
| dy | G | kG | dy | w |
| = | × 1 × 104 = 0.5 × 104 K/m | |
| 1.1 |
