Question

a)

 The temperature of 200 g of water increases from 20°C to 50°C in 10 minutes. Calculate:

 

 

i.

the amount of heat gained by the water.  

 

 

ii.

the average rate at which the water is gaining heat.    

 

 

             (Specific heat capacity of water = 4200 J kg^{-1 O}C^-1)

 

b) Determine the amount of heat that must be removed from 1 kg of water at 40°C to convert it to ice at -5°C.

 

Answer 1

(a)

i. the amount of heat gained by the water

$$Q=cm\Delta T\\ =4200*0.200*30=25200\:\rm J$$

ii. the average rate at which the water is gaining heat

$$P=\frac{Q}{t}=\frac{25200}{10*60}=42\:\rm W$$

(b)

$$Q=Q_1+Q_2+Q_3\\ =c_wm\Delta T_1+\lambda m+c_{ice}m\Delta T_2$$

$$Q=4200*1*40+330000*1+2100*1*5\\ =5.1*10^5\:\rm J$$