The quantities of heat required to raise the | vedclass

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(B) The heat required to change the temperature of a body is given by the formula $\Delta Q = M s \Delta T$,where $M$ is the mass,$s$ is the specific

Vedclass · Accepted Answer

$27/8$

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(B) The heat required to change the temperature of a body is given by the formula $\Delta Q = M s \Delta T$,where $M$ is the mass,$s$ is the specific heat capacity,and $\Delta T$ is the change in temperature.Since both spheres are made of copper,the specific heat capacity $s$ is the same for both.Given that the temperature change $\Delta T = 1 \ K$ is the same for both,we have $\Delta Q \propto M$.The mass $M$ of a sphere is given by $M = V \rho = \frac{4}{3} \pi r^3 \rho$,where $V$ is the volume,$r$ is the radius,and $\rho$ is the density.Since $\rho$ is the same for both copper spheres,$M \propto r^3$.Therefore,the ratio of heat required is $\frac{\Delta Q_1}{\Delta Q_2} = \frac{M_1}{M_2} = \left( \frac{r_1}{r_2} \right)^3$.Given $r_1 = 1.5 r_2$,we have $\frac{r_1}{r_2} = 1.5 = \frac{3}{2}$.Thus,$\frac{\Delta Q_1}{\Delta Q_2} = \left( \frac{3}{2} \right)^3 = \frac{27}{8}$.

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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