Question

Imagine that you have two cups, one containing 1900 g of water and the other one containing 2400 g of an unknown liquid. The specific heat of water is 4.19 J/g·°C, and the specific heat of the unknown liquid is 8.07 J/g·°C. You use two identical immersion heaters to heat the water and the unknown liquid simultaneously. Assume that all the heat from the heater is used to heat the content of the cups.

(a) You started heating the water and the unknown liquid at the same time. If the temperature of the water was increased from 24.4 °C to 37.5 °C, for the same time period how high temperature was the unknown liquid heated to? The initial temperature of the unknown liquid was the same as the water when you started heating.

____ degrees C

(b) If the heating described in part (a) was for the duration of 11 minutes, what was the power of the heaters you used?

____W

Answer 1

Since the heaters are identical thus they will provide exactly same amount of heat in the same time to both the water and unknown liquid.

Now by the heat provided by the heater, temperature of water increased from 24.4 degree celsius to 37.5 degree celsius. then using the formula for heat gained and using the fact of identical heaters,

   (Since both liquid and water is at same initial temperature)

Using all given values in above,

  

  

  

(ANS)

b). Power of heater= Heat provided/ Time Taken

then   

Using all in SI units and using the fact that both heaters are identical hence heat provided by both will be same hence power of both will be same.

  

  (ANS)