Question

An object at 27°C has its temperature increased to 37°C.

Answer 1

Answer:

b. 14

Explanation:

$T_{i}$ = Initial temperature = 27 °C = 27 + 273 = 300 K

$T_{f}$ = Final temperature = 37 °C = 37 + 273 = 310 K

$P_{i}$ = Initial Power radiated by the object

$P_{f}$ = Final Power radiated by the object

We know that the power radiated is directly proportional to fourth power of the temperature. hence

$\frac{P_{f}}{P_{i}} = \frac{T_{f}^{4} }{T_{i}^{4} }\\\frac{P_{f}}{P_{i}} = \frac{(310)^{4} }{(300)^{4} }\\\frac{P_{f}}{P_{i}} = 1.14\\P_{f} = (1.14) P_{i}$

Percentage increase in power is given as

$\frac{(P_{f} - P_{i})\times100}{P_{i}} \\\frac{((1.14) P_{i} - P_{i})\times100}{P_{i}} \\14$