Question

The quantities of heat required to raise the temperatures of two solid steel spheres of r and 2r respectively through 1 K each are in the ratio of​

Answer 1

Given;

• Radius of sphere 1 is r and sphere 2 is 2r.  

To find;

• Ratio of heats(Q) req  to raise temperature of spheres by 1 K.

Solution;

• We know that, Q = Mass × Specific Heat capacity × Δtemperature.
• ∴ Q = m × h × Δt.
• Both spheres are made of steel. So their specific heat capacity will be same and will get cancelled in ratio.
• Δ t is 1K for both spheres. Hence even that will be cancelled in ratio.
• Mass = Volume × density    
• Taking ratio of Q1 and Q2 we get

            $\frac{Q_1}{Q_2} = \frac{Volume_1 * Density_1}{ Volume_2 * Density_2}$    

• Density of both spheres is same since material is same and so it gets cancelled in ratio.
• Volume of sphere = 4/3 (π× r³).

              ∴    $\frac{Q_1}{Q_2} = \frac{\frac{4 \pi r_1^3 }{3} }{ \frac{4 \pi r_2^3}{3} } =( \frac{r_1}{r_2} )^3$  

               ∴ $\frac{Q_1}{Q_2} =( \frac{r}{2r} ) ^3 = (\frac{1}{2} )^3 = \frac{1}{8}$