Transmission Of Heat Question 340
Question: One day in a room a heater connected to supply maintained temperature $ 20{}^\circ C $ when outside temperature was $ -20{}^\circ C $ . Another day with the same heater, in the same room, temperature was $ 10{}^\circ C $ when outside temperature was $ -40{}^\circ C $ . If temperature of heater is same both the days. Find this value. (use $ \frac{dT}{dt}=k(T-T _{0}) $ and k is same for both days).
Options:
A) $ 120{}^\circ C $
B) $ 30{}^\circ C $
C) $ 40{}^\circ C $
D) $ 60{}^\circ C $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] $ mS( \frac{dT}{dt} ),=,ka,A,({\theta _{in}}-{\theta _{out}}) $ at the heater at the wall $ k,(\theta -20)=k’,A,(20+20) $ $ k,(\theta -10)=k’,A,(10+40) $ $ \frac{\theta -20}{\theta -10}=\frac{40}{50} $ $ 5\theta -100=4\theta $ $ \theta =60{}^\circ C $
BETA
