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) Given:

$m=\rm 0.2\: kg$

$c=4200\:\rm J/(kg\ ^\circ C)$

t_i=\rm 20\: ^\circ C

t_f=\rm 50\: ^\circ C

$\tau=\rm 10\: min=600\: s$

(i)

$$Q=cm(t_f-t_i)$$

$$Q=4200*0.2*(50-20)=25200\:\rm J$$

(ii)

$$P=\frac{Q}{\tau}=\frac{25200}{600}=42\:\rm W$$