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10-1.Thermometry, Thermal Expansion and Calorimetry
medium
Two spheres made of same substance have diameters in the ratio $1 : 2.$ Their thermal capacities are in the ratio of
A
$1:2$
B
$1:8$
C
$1:4$
D
$2:1$
Solution
(b)Thermal capacity $=$ Mass $\times$ Specific heat
Due to same material both spheres will have same specific heat.
Also mass = Volume (V) $\times$ Density ($\rho$)
Ratio of thermal capacity
$ = \frac{{{m_1}}}{{{m_2}}} = \frac{{{V_1}\rho }}{{{V_2}\rho }} = \frac{{\frac{4}{3}\pi r_1^3}}{{\frac{4}{3}\pi r_2^3}} = {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^3} = {\left( {\frac{1}{2}} \right)^3} = 1:8$
Standard 11
Physics
