Question:
The ratio of radii of two spheres of same material is $1 : 4$, then the ratio of their heat capacities is
The ratio of radii of two spheres of same material is $1 : 4$, then the ratio of their heat capacities is
Updated On: Jul 28, 2022
- $ \frac{1}{4} $
- $ \frac{1}{16} $
- $ \frac{1}{32} $
- $ \frac{1}{64} $
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The Correct Option is D
Solution and Explanation
Heat capacity
$H=m s=\frac{4}{3} \pi r^{3} \rho s$
For same material, density $\rho$ and specific heat $s$ are same, so heat capacity
$H \propto r^{3}$
Hence, the ratio of heat capacities is
$\frac{H_{1}}{H_{2}}=\left(\frac{r_{1}}{r_{2}}\right)^{3}=\left(\frac{1}{4}\right)^{3}=\frac{1}{64}$
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Concepts Used:
Specific Heat Capacity
Specific heat of a solid or liquid is the amount of heat that raises the temperature of a unit mass of the solid through 1°C.
Molar Specific Heat:
The Molar specific heat of a solid or liquid of a material is the heat that you provide to raise the temperature of one mole of solid or liquid through 1K or 1°C.
Specific Heat at Constant Pressure or Volume:
The volume of solid remains constant when heated through a small range of temperature. This is known as specific heat at a constant volume. It is denoted as CV.
The pressure of solid remains constant when heated through a small range of temperature. This is known as specific heat at constant pressure which can be denoted as CP.