General Thermal/Energy Physics Problem

[Timiop2008]

The Plug of a new steel, electric kettle says "power rating 2.5W"

a) The metal wall of the kettle and the water inside the kettle always remain close to thermal equilibrium, even when the water boils. Explain how this is true.

b) The kettle uses 300J to raise its temperature by 1 Kelvin. 0.75Kg of water with specific heat capacity 4200 JKgK is heated from 20'C to 100'C. Calculate the energy transferred during the process and state two assumptions you have made.

c) Calculate the time the process takes

 

[Stonebridge]

You need to show your attempt at this, and explain where you are having a problem, before you can receive help.

 

[kerimek]

a) This is true because of the principle of thermal equilibrium, which states that when two objects are in contact with each other, they will eventually reach the same temperature. In the case of the electric kettle, the metal walls and the water inside are in constant contact, allowing for the transfer of thermal energy between them. As the water is heated, it transfers its thermal energy to the metal walls, and as the metal walls cool down, they transfer their thermal energy back to the water, maintaining a state of thermal equilibrium.

b) The energy transferred during the process can be calculated using the formula Q = mcΔT, where Q is the energy transferred, m is the mass of the water, c is the specific heat capacity, and ΔT is the change in temperature. Plugging in the given values, we get Q = (0.75kg)(4200 JKgK)(80 K) = 252,000 J.

Two assumptions made in this calculation are that the specific heat capacity of water remains constant throughout the heating process and that there is no heat loss to the surroundings.

c) The time the process takes can be calculated using the formula t = Q/P, where t is the time, Q is the energy transferred, and P is the power rating of the kettle. Plugging in the values, we get t = 252,000 J / 2.5 W = 100,800 seconds. However, this calculation assumes that all the energy transferred is used to heat the water, which may not be the case due to heat loss to the surroundings. Thus, the actual time may be slightly longer.