The question is the following:
You would like to have a cup of tea, so you need to heat up water. In this exercise, you do that by putting water (0.5 liter) in a cooker that is electrically heating up its content.
The water out of the tap is 20oC. The question here is: how long does the cooker need to be switched in order for the water to reach a temperature of 80oC?
Negelect the heat capacity of the cooker. Furthermore, ignore heat losses to the surroundings
The specific heat of water is 4200 J/kgK. The electric power of the cooker is 1kW.
I am trying to solve this with dE/dt=heat flow in, where E=mcp(T-To). m is the mass, cp is the specific heat, T is the temp with respect to time, and To is the initial temp. I do not know how to integrate the equation of E with respect to time. Supposedly the To term drops out of the equation but i do not understand why. I know you can separate the variables so dt is on the right hand side and then you get:
mcp*Integral(d(T-To))=heat in * Integral (dt), not sure where to go next due to confusion on the left hand side.
You would like to have a cup of tea, so you need to heat up water. In this exercise, you do that by putting water (0.5 liter) in a cooker that is electrically heating up its content.
The water out of the tap is 20oC. The question here is: how long does the cooker need to be switched in order for the water to reach a temperature of 80oC?
Negelect the heat capacity of the cooker. Furthermore, ignore heat losses to the surroundings
The specific heat of water is 4200 J/kgK. The electric power of the cooker is 1kW.
I am trying to solve this with dE/dt=heat flow in, where E=mcp(T-To). m is the mass, cp is the specific heat, T is the temp with respect to time, and To is the initial temp. I do not know how to integrate the equation of E with respect to time. Supposedly the To term drops out of the equation but i do not understand why. I know you can separate the variables so dt is on the right hand side and then you get:
mcp*Integral(d(T-To))=heat in * Integral (dt), not sure where to go next due to confusion on the left hand side.