The quantities of heat required to raise the | vedclass

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(A) The heat required to raise the temperature of a body is given by $Q = mc\Delta T$,where $m$ is the mass,$c$ is the specific heat capacity,and $\De

Vedclass · Accepted Answer

$27/8$

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(A) The heat required to raise the temperature of a body is given by $Q = mc\Delta T$,where $m$ is the mass,$c$ is the specific heat capacity,and $\Delta T$ is the change in temperature.Since the spheres are made of the same material (copper),$c$ is constant. For a given $\Delta T = 1 \ K$,$Q \propto m$.The mass $m$ of a sphere is given by $m = \rho V$,where $\rho$ is the density and $V$ is the volume.$V = \frac{4}{3}\pi r^3$,so $m \propto r^3$.Therefore,$Q \propto r^3$.The ratio of heat required is $\frac{Q_1}{Q_2} = \frac{r_1^3}{r_2^3} = \left(\frac{r_1}{r_2}\right)^3$.Given $r_1 = 1.5 r_2$,we have $\frac{r_1}{r_2} = 1.5 = \frac{3}{2}$.Thus,$\frac{Q_1}{Q_2} = \left(\frac{3}{2}\right)^3 = \frac{27}{8}$.

The quantities of heat required to raise the temperatures of two copper spheres of radii $r_{1}$ and $r_{2}$ $(r_{1} = 1.5 r_{2})$ through $1 \ K$ are in the ratio of:

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