The quantities of heat required to raise the temperature of two solid copper spheres of radii r1 and r2 (r1 = 1.5 r2) through 1 K are in the ratio :

Question

The quantities of heat required to raise the temperature of two solid copper spheres of radii r1 and r2 (r1 = 1.5 r2) through 1 K are in the ratio : (A)  (27/8) (B)  (9/4) (C)  (3/2) (D)  (5/3)

Tardigrade Admin · Accepted Answer

Heat supplied Δ Q =MS Δ T For same material âsâ remains the same Δ Q propto M and M=(4/3)π r3 ρ ⇒ (Δ Q1/Δ Q2) =((r1/r2))3 =((1.5/1))3 =(27/8)

Q. 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 :

$\frac{27}{8}$

$\frac{9}{4}$

$\frac{3}{2}$

$\frac{5}{3}$

Heat supplied $Δ Q = MS Δ T$
For same material ‘s’ remains the same
$Δ Q \propto M$ and $M = \frac{4}{3} π r^{3} ρ$
$\Rightarrow \frac{Δ Q _{1}}{Δ Q _{2}}$
$= (\frac{r _{1}}{r _{2}})^{3}$
$= (\frac{1.5}{1})^{3}$
$= \frac{27}{8}$

Q. The quantities of heat required to raise the temperature of two solid copper spheres of radii r1​ and r2​ (r1​=1.5r2​) through 1 K are in the ratio :

827​

49​

23​

35​