At a lecture in Cork in 1843, James Joule, while describing his work on heat and temperature, suggested the principle of conservation of energy - Leaving Cert Physics - Question 7 - 2016

Using the gravitational potential energy formula:

$E = mgh$

where:

• $E$ is the energy converted into heat,
• $m$ is the mass of the water dimensioned by density,
• $g$ is the acceleration due to gravity (9.8 m/s²),
• $h$ is the height of the Niagara Falls.

To find $h$, suppose we can consider the temperature difference that contributes to energy: $E = mc heta$

We have:

• $heta = 0.12 °C$ (the temperature difference),
• $c = 4200 \text{ J kg}^{-1} \text{ K}^{-1}$ (specific heat capacity of water).

Setting the two equations equal:

$mgh = mc heta$

Thus: $h = \frac{c\theta}{g} = \frac{4200 \times 0.12}{9.8} \approx 51.4 \text{ m}$

A heat pump operates by transferring thermal energy from a colder area to a warmer area. It uses a fluid that absorbs heat from the cold area (inside the refrigerator) and releases it in another area (exterior) via components like a compressor and a condenser.

In the context of a refrigerator, the fluid circulates, absorbs heat from the internal environment, and is compressed to raise its temperature before dissipating the heat outside, thereby lowering the temperature inside the refrigerator.

• High (specific) latent heat of vaporisation to maximize heat absorption during phase change.
• Low boiling point / volatile / low molecular mass to allow for efficient energy transfer at lower temperatures.

Using the latent heat formula:

$E = mL$

where:

• $E = 12 \text{ kJ} = 12000 \text{ J}$,
• $L = 4.6 \text{ MJ kg}^{-1} = 4600000 \text{ J kg}^{-1}$.

Thus the mass $m$:

$m = \frac{E}{L} = \frac{12000}{4600000} = 0.0026 \text{ kg}.$

Using the specific heat formula:

$E = mc\Delta T$

where:

• $m = 0.74 \text{ kg}$,
• $E = 12000 \text{ J}$,
• $c = 1005 \text{ J kg}^{-1} K^{-1}$.

Rearranging for $Delta T$ gives:

$\Delta T = \frac{E}{mc} = \frac{12000}{0.74 \times 1005} \approx 16.1 °C.$