Question

A copper ball of mass $100g$ is at a temperature $T$. It is dropped in a copper calorimeter of mass $100g$, filled with $170g$ of water at room temperature. Subsequently, the temperature of the system is found to be ${75}^{\circ }C$. $T$ is given by (Given: room temperature $={30}^{\circ }C$, specific heat of copper $=0.1cal/g^{\circ }C$)

• A. ${800}^{\circ }C$
• B. ${825}^{\circ }C$
• C. ${1250}^{\circ }C$
• D. ${885}^{\circ }C$

Answer 1

The correct option is D ${885}^{\circ }C$

We know that: $Q=ms\Delta \theta$
Given: $m_c=100g,s_c=0.1cal/g^{\circ }C,$
$m_w=170g,{\theta }_0={30}^{\circ }C,s_w=1cal/g^{\circ }C$

Heat given $=$ Heat taken (By water and calorimeter)

$m_c{s}_c(T-75)$

$=m_w{s}_w(75-30)+m{s}_c(75-30)$
$\left(100\right)\left(0.1\right)(T-75)=\left(100\right)\left(0.1\right)\left(45\right)+\left(170\right)\left(1\right)\left(45\right)$

$10(T-75)=450+7650=8100$

$T-75=810$

$T={885}^{\circ }C$

Final Answer: (d)