The quantities of heat required to raise the tempratures of two copper spheres of radii `r_(1)`
`r_(2)` (`r_(1)=1.5r_(2)`) through 1 K are in the ratio of

Options

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

Answer

A

Explanation

Here ,`r_(1)=1.5r_(2)(3)/(2)r_(2)`
Quantity of heat required to raise the temperature of copper sphere of radius `r_(1)` through 1 K is `Q_(1)=m_(1)S_(Copper)DeltaT`
=`((4)/(3)pi_(1)^(3)rhoCopper)xxs_(Copper)xx1`
`Q_(1)=(4)/(3)pir_(1)^(3)rho_(Copper)S_(Copper)`
Quantity of heat rwequired to raise he temprature of copper sphere of radius `r_(2)` through 1K is
`Q_(2)=M_(2)S_(Copper)DeltaT`
=`(4)/(3)pir_(2)^(3)rho_(Copper)xxS_(copper)xx1`
`=(4)/(3)pir_(2)^(3)rho_(Copper)S_(Copper)`......(ii)
Divide (i) by (ii), We get
`(Q_(1))/(Q_(1))=((r_(1))/(r_(2)))^(3)=((3)/(2))^(3)=(27)/(8)``(Q_(1))/(Q_(1))=((r_(1))/(r_(2)))^(3)=((3)/(2))^(3)=(27)/(8)`