Question
We need to store 1l of cold water in warm weather for as long as possible. In which of the following shapes should a flask be built for the task. Assume the thickness and material are same for all the shapes.
Answer: Option C
:
C
For all modes of heat transfer ΔQ∝Area,A.So we should choose the shape with minimum area for minimum heat transfer.
(a)For cubical:
Volume, V = a3=1l,∴a=1dm(decameter)
Area, A = 6a2=6dm2
(b)For conical: V= πr2h3, but given r=h,r=313π dm
A=πr(√2r)+πr2
= 7.354 dm2
(c)For Sphere:
V=43πr3, ∴r=(34)13dm
A=4πr2=4.84dm2
(d) For Cylinder:
V=π×r2×r∴r=1π13dm
A=2πr2+2πr.r=5.86dm2
As Sphere has the least area among these, it will be the shape with minimum heat loss. In fact sphere is the shape with the minimum surface area among all possible shapes!
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:
C
For all modes of heat transfer ΔQ∝Area,A.So we should choose the shape with minimum area for minimum heat transfer.
(a)For cubical:
Volume, V = a3=1l,∴a=1dm(decameter)
Area, A = 6a2=6dm2
(b)For conical: V= πr2h3, but given r=h,r=313π dm
A=πr(√2r)+πr2
= 7.354 dm2
(c)For Sphere:
V=43πr3, ∴r=(34)13dm
A=4πr2=4.84dm2
(d) For Cylinder:
V=π×r2×r∴r=1π13dm
A=2πr2+2πr.r=5.86dm2
As Sphere has the least area among these, it will be the shape with minimum heat loss. In fact sphere is the shape with the minimum surface area among all possible shapes!
Was this answer helpful ?
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