0.1.1 Explain what is meant by specific latent heat of fusion - AQA - A-Level Physics - Question 1 - 2018 - Paper 2

First, we need to calculate the total energy transferred by the heater in 1 hour. The power of the heater is 2.7 kW, which means:

$ext{Energy} = ext{Power} imes ext{Time} = 2.7 imes 10^3 ext{ W} imes 3600 ext{ s} = 9720 imes 10^3 ext{ J}$

Next, we will determine the mass of the water in the hot tub:

$ext{Volume} = 4.5 ext{ m}^3\ ext{Density} = 1000 ext{ kg m}^{-3}\ ext{Mass} = ext{Volume} imes ext{Density} = 4.5 imes 1000 = 4500 ext{ kg}$

Now we can use the formula for heat transfer:

$Q = m c riangle T$

Where:

• Q is the total energy (J)
• m is the mass of the water (kg)
• c is the specific heat capacity (J kg⁻¹ K⁻¹)

( riangle T) is the change in temperature (K)

Rearranging gives:

$riangle T = \frac{Q}{m c} = \frac{9720 imes 10^3}{4500 imes 4200} = 0.51 ext{ K}$

Therefore, the rise in temperature is approximately 0.51 °C.

When the pump circulates water at higher speeds, it increases the rate at which hot water is distributed throughout the hot tub. This leads to a quicker uniform temperature rise because the water is exposed to the heater more frequently, allowing it to absorb heat more efficiently. As a result, the overall system can maintain a higher temperature compared to slower pump speeds.