A solid copper sphere (density rho and specific heat capacity c ) of radius r at an initial temperature 200K is suspended inside a chamber

Q: A solid copper sphere (density $\rho $ 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 $\mu s$) for the temperature of the sphere to drop to $100\, K$ is

b (b) $\frac{{dT}}{{dt}} = \frac{{\sigma \,A}}{{mcJ}}\,\,({T^4} - T_0^4)$ [In the given problem fall in temperature of body $dT = (200 - 100) = 100K$, temp. of surrounding $T0 = 0K$ , Initial temperature of body $T = 200K].$ $\frac{{100}}{{dt}} = \frac{{\sigma 4\pi {r^2}}}{{\frac{4}{3}\pi {r^3}\rho \,c\,J}}({200^4} - {0^4})$ ==> $dt = \frac{{r\rho \,c\,J}}{{48\sigma }} \times {10^{ - 6}}s = \frac{{r\rho \,c}}{\sigma }.\frac{{4.2}}{{48}} \times {10^{ - 6}}$ $ = \frac{7}{{80}}\frac{{r\rho \,c}}{\sigma }\mu \,s\tilde --\frac{7}{{72}}\frac{{r\rho \,c}}{\sigma }\mu \,s$ [As $J = 4.2$ ]

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

A solid copper sphere (density $\rho $ 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 $\mu s$) for the temperature of the sphere to drop to $100\, K$ is

A$\frac{{72}}{7}\frac{{r\rho c}}{\sigma }$
B$\frac{7}{{72}}\frac{{r\rho c}}{\sigma }$
C$\frac{{27}}{7}\frac{{r\rho c}}{\sigma }$
D$\frac{7}{{27}}\frac{{r\rho c}}{\sigma }$

IIT 1991, Diffcult

STD 11 Science
NEET
STD 11 - 10.2. transmission of heat
Physics

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