A solid copper sphere (density ρ and specific heat capacity (c) of radiu

Discussion Forum : Heat Transfer

Question -

A solid copper sphere (density $ρ$ and specific heat capacity (c) of radius r at an initial temperature 200K is suspended inside a chamber whose walls are at almost 0K. The time required (in $μ$ s) for the temperature of the sphere to drop to 100 K is

Options:

A .

\frac{80}{7} \frac{r ρ c}{σ}

B .

\frac{7}{80} \frac{r ρ c}{σ}

C .

\frac{27}{7} \frac{r ρ c}{σ}

D .

\frac{7}{27} \frac{r ρ c}{σ}

Answer: Option B
:
B

\frac{d T}{d t} = \frac{σ A}{m c J} (T^{4} - T_{0}^{4})

[In the given problem fall in temperature of body dT=(200-100)=100K , temp. of surrounding

T_{0} = 0 K

, Initial temperature of body T=200k].

\frac{100}{d t} = \frac{σ 4 π r^{2}}{\frac{4}{3} π r^{3} ρ c J} (200^{4} - 0^{4})

\Rightarrow d t = \frac{r ρ c J}{48 σ} \times 10^{- 6} s = \frac{r ρ c}{σ} . \frac{4.2}{48} \times 10^{- 6}

[As J = 4.2]

\frac{7}{80} \frac{r ρ c}{σ} μ s

Was this answer helpful ?

Next Question

Discussion Forum : Heat Transfer

Submit Your Solution hear: