Question

You have 250 g of water in an aluminium calorimeter with a mass of 125 g. How
long will it take to increase the temperature of the water and calorimeter from 20C to 37C if the system is heated by a resistive heating element with 8 V across the resistor and 0.75 A flowing through the resistor?

Answer 1

To answer this question, you need to break it into two parts. Energy = Power*Time (E=P*t). Therefore time = Energy/Power (t=E/P). E and P are what we need to work out:

Power = Voltage*Current (P=V*i)

When heat is added to a solid or a liquid, that energy increases the materials internal energy and thus increases its temperature. The relationship between the heat added and the resulting change in temp is given by:

E=Q(Water) + Q(cup)
Q=m*c*change in temp
Q= heat energy
m= mass
c= specific heat. These aren't given in your question, but are easily found online. c(water)=4184J
and c(aluminum)=900J

So the total energy dissipated as heat = The heat dissipated in the water + heat dissipated in the cup.

E=0.125*900*17 + 0.25*4184*17
=1912.5 + 17782
=19694.5J

Now, we can solve for the final answer:

t= E/P
= 19694.5/6
= 3282.4s
= 54.7 minutes