1. 27/8 2. 9/4 3. 3/2 4. 5/3

Answer: 1. 27/8 Heat needed for a 1 K rise is Q=mcΔ T . Both spheres are copper, so c is the same and Q∝ m∝ r³ . Q₁/Q₂=(r₁/r₂)³=(1.5)³=27/8 Answer: option 1.

Topic: Specific heat capacity, calorimetry, change of state, latent heat· Properties of Solids and Liquids

The quantities of heat required to raise the temperature of two solid copper spheres of radii r_1 and r_2 (r_1 = 1.5 r_2) through 1 K are in the ratio :

1. $\frac{27}{8}$

2. $\frac{9}{4}$

3. $\frac{3}{2}$

4. $\frac{5}{3}$

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Answer: 1. $\frac{27}{8}$

Heat needed for a 1 K rise is $Q=mc\Delta T$. Both spheres are copper, so $c$ is the same and $Q\propto m\propto r^3$.

$$\frac{Q_1}{Q_2}=\left(\frac{r_1}{r_2}\right)^3=(1.5)^3=\frac{27}{8}$$

Answer: option 1.

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The quantities of heat required to raise the temperature of two solid copper spheres of radii r_1 and r_2 (r_1 = 1.5 r_2) through 1 K are in the ratio :

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