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 1K are in ratio

Options

A. `(27)/(8)`
B. `(9)/(4)`
C. `(3)/(2)`
D. 1

Answer

A

Explanation

Here, `r_(1) = 1.5 r_(2) = (3)/(2) r_(2) rArr (r_(1))/(r_(2)) =(3)/(2)`
Quantity of heat required to raise the temperature of copper sphere of radius `r_(1)` through 1K is
`Q_(1) = m_(1) s_("Copper") Delta T = ((4)/(3) pi r_(1)^(3)) rho_("Copper") xx s_("Copper") xx 1`
or `Q_(1) = (4)/(3) pi r_(1)^(3) rho_("Copper") s_("Copper")` ....(i)
Quantity of heat required to raise the temperature of copper sphere of radius `r_(2)` through 1K is
`Q_(2) = m_(2) s_("Copper") Delta T = (4)/(3) pi r_(2)^(3) rho_("Copper") xx s_("Copper") xx 1`
or `Q_(2) = (4)/(3) pi r_(2)^(3) rho_("Copper") s_("Copper")` ..(ii)
Divide (i) by (ii), we get `(Q_(1))/(Q_(2)) = ((r_(1))/(r_(2)))^(3) = ((3)/(2))^(3) = (27)/(8)`