Chapter 14, Problem 66GP

To determine

To find: Temperature of 150W bulb.

Answer to Problem 66GP

Temperature of 150W bulb is ${112}^{°}\text{C}$ .

Explanation of Solution

Given:

Power rating of bulb1, $P_1=60\text{W}$

Temperature of bulb $1,T_1={65}^{\circ }\text{C}$

Power rating of bulb2, $P_2=150\text{W}$

Temperature of bulb2, $=T$

Room Temperature $T_2={(273+18)}^{\circ }\text{C}={291}^{\circ }\text{C}$

  $90\text{\%}$ of energy is emitted at heat, therefore net flow of heat energy for bulb (1)

  $\begin{array}{l}P.\text{Δ}t=e\sigma A\left(T_1^4-T_2^4\right)\\ =\left({338}^4-{291}^4\right)\\ 0.90\times 60\text{W}.\text{Δ}t=\left({338}^4-{291}^4\right)--(1)\\ 0.90\times 150\text{W}\cdot \text{Δ}t=\left(T^4-{291}^4\right)--(2)\end{array}$

Dividing equation (2) by (1)

  $\begin{array}{l}\frac{15\cancel{0}}{6\cancel{0}}=\frac{T^4-{291}^4}{{338}^4-{291}^4}\\ \frac{15}{6}=\frac{T^4-{291}^4}{5.88\times {10}^9}\\ T^4-{291}^4=1.47\times {10}^{10}\\ T=385K\\ ={112}^{°}\text{C}\end{array}$

Temperature of 150W bulb is ${112}^{°}\text{C}$ .