Question

An object of mass $8\text{kg}$ falls through a height of $60\text{m}$ and by means of a mechanical linkage, rotates a paddle wheel that stirs $0.8\text{kg}$ of water. Determine the change in temperature of water if initial temperature was ${15}^{\circ }\text{C}$. Assume no heat is lost to surroundings, specific heat of water, $c=4190\text{J/kg}{}^{\circ }\text{C})$.

• A. ${0.5}^{\circ }\text{C}$
• B. ${1.4}^{\circ }\text{C}$
• C. ${2.1}^{\circ }\text{C}$
• D. ${3.6}^{\circ }\text{C}$

Answer 1

The correct option is B ${1.4}^{\circ }\text{C}$

Given that
Mass of object $\left(m\right)=8\text{kg}$
Height of fall $\left(h\right)=60\text{m}$
Mass of water $\left(m_w\right)=0.8\text{kg}$
Initial temperature $T_i={15}^{\circ }\text{C}$
Loss of mechanical energy $E=mgh$
Change in temperature of water $=\Delta T$
Thermal energy gained by water $E=m_{w}c\Delta T$

From law of conservation of energy,
$m_{w}c\Delta T=mgh$
$\Rightarrow \Delta T=\frac{mgh}{m_{w}c}$
$\Rightarrow \Delta T=\frac{8\text{kg}\times 9.8{\text{m/s}}^2\times 60\text{m}}{0.8\text{kg}\times \left(4190\text{J/kg}{}^{\circ }\text{C}\right)}$
$\Rightarrow \Delta T={1.4}^{\circ }\text{C}$
Hence, the answer $\left(b\right)$ is correct.