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A heated solid copper sphere (of surface area $A$ and volume $V$) is immersed in a large body of cold fluid. Assume the resistance to heat transfer inside the sphere to be negligible and heat transfer coefficient $(h)$, density $(\rho)$, heat capacity $(C)$, and thermal conductivity $(k)$ to be constant. Then, at time $t$, the temperature difference between the sphere and the fluid is proportional to:

  1. $exp\left [ -\frac{hA}{\rho VC}t \right ]$
  2. $exp\left [ -\frac{\rho VC}{hA}t \right ]$
  3. $exp\left [ -\frac{4\pi k}{\rho CA}t \right ]$
  4. $exp\left [ -\frac{-\rho CA}{4\pi k}t \right ]$
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