Properties Of Solids And Liquids Question 451
Question: The room heater can maintain only $ 16{}^\circ C $ in the room when the temperature outside is $ -20{}^\circ C $ . It is not warm and comfortable, that is why the electric stove with power of 1 kW is also plugged in. Together these two devices maintain the room temperature of $ 22{}^\circ C $ . Determine the thermal power of the heater.
Options:
A) 3 kW
B) 4 kW
C) 5 kW
D) 6 kW
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Answer:
Correct Answer: D
Solution:
[d] Rate of heat loss with only room heater $ Ph=\frac{\Delta Q}{\Delta t}=C( 16+20 ), C= constant $ while for both heater and stove it is $ p _{h}+p _{s}={{( \frac{\Delta Q}{\Delta t} )}^{’}}=C( 22+20 ) $
$ \frac{p _{h}}{p _{h}+p _{s}}=\frac{36}{42}\Rightarrow 7p _{h}=6p _{s}+6p _{h} $
$ \Rightarrow p _{h}=6p _{s}=6\text{kW} $
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