# In Joule's experiment, a mass of 6 kg falls through a height of 50 m and rotates the paddle wheel...

## Question:

In Joule's experiment, a mass of 6 kg falls through a height of 50 m and rotates the paddle wheel which stirs 0.6 kg of water. If the initial temperature of the water is 15 degrees C, find the rise in temperature. ( g = 9.8 m/s{eq}^2 {/eq})

## Specific heat capacity:

To raise a temperature of any substance, it will require some amount of the energy, this energy is called as the specific heat capacity.

The specific heat capacity capacity is formulated as:

$$\color{red}{c=\frac{\Delta E}{m\Delta T}}$$

Thus in technical terms the amount of energy required to raise the temperature of {eq}m=1 \ \text{kg} {/eq} substance by {eq}\Delta T=1^{\circ} C {/eq}.

Given:

• A mass {eq}m=6 \ \text{kg} {/eq} falls from a height {eq}h=15 \ \text{m} {/eq}
• The mass of water stirring by the paddle wheel {eq}m_1=0.6 \ \text{kg} {/eq}
• The initial temperature of the water {eq}T_1=15^{\circ} C {/eq}

Now recall that from the energy conservation, the potential energy of the mass at height h is responsible to the change in temperature of the water, Thus:

{eq}\displaystyle{m_1c(T_2-T_1)=mgh \ \left(\text{c=specific heat of water}=4186 \ \frac{\text{J}}{\text{kg}{^\circ}\text{C}}\right)} {/eq}

Thus the final temperature of the water is:

{eq}\begin{align} T_2&=\frac{mgh}{m_1 c}+T_1\\ &=\frac{6\times9.8\times50}{0.6\times4186}+(15^{\circ} C)\\ &=1.171^{\circ} C+15^{\circ} C\\ &=\color{blue}{16.171^{\circ} C} \end{align} {/eq} 