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I had a perception that rate of cooling and rate of heat loss are synonymous because the rate at which it looses heat indicates the rate at which it is cooling but this question changed my view

There are eight identical solid spheres at same temperature, the rate of cooling of each sphere is x. The rate of heat loss from each sphere is Q. All spheres are combined to form a single sphere at same temperature then for new sphere

Since the answer is different for both the rates there must be a difference in both terminologies which I'm not able to get.

I'm aware of stefan formula which says $dq/dt = \sigma$ $\epsilon$A$T^4$ taking atmospheric temp 0 And one result of newtons formula k=$ \sigma$ $\epsilon$A$T^3$ $/ms$ Where s is specific heat

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If the rate of cooling is surface-area dependent, as is the case for convection, for example, then things would obviously change when eight spheres are combined into one, as the total surface area has changed. Is this what you're asking about?

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  • $\begingroup$ Ya is there a formula differentiating the two terms $\endgroup$
    – imposter
    Commented Dec 29, 2020 at 17:50
  • $\begingroup$ If this answers your question, then please mark it as useful. If not, please add as much clarifying information as you have. $\endgroup$
    – Chemomechanics
    Commented Dec 29, 2020 at 17:51
  • $\begingroup$ I've made a change $\endgroup$
    – imposter
    Commented Dec 29, 2020 at 17:57
  • $\begingroup$ Since the heat loss (in $\text{W}$ or $\text{J/s}$) depends on the surface area here, then yes, the rate of cooling (in $\text{K/s}$) will depend on whether the mass is arranged in a single sphere (with a surface area of $4\pi r^2$) or $n$ multiple spheres (with a surface area of $4\pi n^{2/3} r^2$). $\endgroup$
    – Chemomechanics
    Commented Dec 29, 2020 at 18:06

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