# In a Joule experiment, a mass of 1.00 kg falls through a height of 50.0 m and rotates a paddle...

## Question:

In a Joule experiment, a mass of 1.00 kg falls through a height of 50.0 m and rotates a paddle wheel that stirs 0.600 kg of water. The water is initially at 15 degrees C. By how much does its temperature rise (in degrees C)?

## Energy Conservation principle:

The energy conservation principle consists of a physical law that states that if no external forces act on the system, the total energy of the system should conserve. Energy is not created nor destroyed, it only transforms. This means that a system may present energy transformations, but the overall total energy of the system will remain the same. The total energy of a system can be determined by the sum of the total kinetic and potential energy of the system.

In order to determine the change in temperature, we must determine the total energy that will be absorbed by the water. Using energy conservation mechanics, the total energy stored within the mass will convert to work that will raise the temperature of the water inside the tank.

Initially, the total energy stored within the system will consist of the potential energy stored within the mass.

{eq}U_e=mgh\\ U_e=1\times9.8\times50\\ U_e=490\ J {/eq}

We use this to calculate the change in temperature experimented by the water. We have the following information:

• Heat: {eq}Q=490\ J {/eq}
• Mass of water: {eq}m=0.600\ kg {/eq}
• initial temperature: {eq}T_i=15^\circ C {/eq}
• Heat capacity of water: {eq}c_p=4.186\ J7kg.^\circ C {/eq}

Solving for temperature:

{eq}Q=mc_p\Delta T\\ 490\ J=0.6\ kg\times4.186\ J/kg^\circ C\times(T_f-15)^\circ C\\ 490=2.51T_f-37.67 \\ 2.51T_f=527.67\\ T_f=210.23^\circ C {/eq} 