Sara has a fire in the fireplace to warm her 20°C apartment. She realizes that she has left the iron poker in the fire. How hot is the fire if the 0.60 m poker lengthens 0.30 cm? (αiron = 12 x 10-6°C-1)
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Answer:
Fire is at temperature of 437°C
Explanation:
Due to heat, the iron rod expands. This phenomenon is called as Linear Thermal Expansion, which is given by the equation:
Δ L / L = α Δ T
Where ,
Δ L is the change in length of the iron poker = 0.3 cm = 0.003 m
L is the Original length of the iron poker = 0.6 m
α is the linear expansion coefficient of iron = 12 x 10^-6 °C^-1
Δ T is the change in temperature.
Δ T = T2- T1
T1 is the initial temperature = 20°C
T2 is the temperature of fire.
So,
T2 - T1 = Δ L / L * α
T2 - 20 = 0.003 / (0.6 * 12 x 10^-6 )
T2 = 417 + 20
T2 = 437 °C
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