KVPY2017PhysicsThermal Properties of Matter
Two bottles A and B have radii R _ A and R _ B and heights h _ A and h _ B respectively with R _ B =2 R _ A and h _ B =2 ~h _ A . These are filled with hot water at 60^ C . Consider that heat loss for the bottles takes place only from side surfaces. If the time the water to cool down to 50^ C is t _ A and t_ B for the bottles A and B , respectively, then t _ A and t_ B are best related as
Options
- At_ A = t _ B
- Bt _ B =2 t _ A
- Ct _ B =4 t _ A
- Dt _ A = t _ A / 2
Correct answer
B. t _ B =2 t _ A
Step-by-step solution
t m A t = k V A = k h t h t _ A t _ B = h _ A h _ B = h ₀ 2 ~h ₀ t _ B =2 t _ A