P27_039.PDF

39.Let R H be the resistance at the higher temperature (800 ◦ C) and let R L be the resistance at the lower

temperature (200 ◦ C). Since the potential diﬀerence is the same for the two temperatures,the power

dissipated at the lower temperature is P L = V 2 /R L ,and the power dissipated at the higher temperature

is P H = V 2 /R H ,so P L =( R H /R L ) P H .Now R L = R H + αR H ∆ T ,where ∆ T is the temperature

diﬀerence T L −

−

600 C ◦ =

−

600 K. Thus,

P L =

R H

R H + αR H ∆ T P H =

P H

1+ α ∆ T =

500 W

= 660 W .

1+(4 . 0

10 − 4 / K)(

−

600 K)

T H =