A kilogram of water (c = 4.186 kJ/kg °C) is stirred using a 400−watt device for 5 minutes. At the end of this time the temperature of the water has increased by 15°C. How much heat was lost to the surroundings?
A) 90.1 kJ
B) 57.2 kJ
C) 82.6 kJ
D) 38.9 kJ

Question

Quizplus · Accepted Answer

The amount of heat gained by water can be calculated using the formula:

Q = mcΔT

where 
Q = heat gained (in Joules) 
m = mass of water (in kg) = 1 kg 
c = specific heat of water (in kJ/kg °C) = 4.186 kJ/kg °C 
ΔT = change in temperature (in °C) = 15 °C

So,

Q = 1 x 4.186 x 15 = 62.79 kJ

Now, the device has used 400 watts of power for 5 minutes = 5 x 60 = 300 seconds.

The total energy used by the device can be calculated using the formula:

E = Pt

where 
E = energy used (in Joules) 
P = power used (in Watts) = 400 W 
t = time (in seconds) = 300 s

So,

E = 400 x 300 = 120000 J = 120 kJ (since 1 kJ = 1000 J)

Since energy can neither be created nor destroyed, the amount of heat lost by water to the surroundings is equal to the amount of energy used by the device, minus the amount of heat gained by water:

heat lost = energy used - heat gained = 120 - 62.79 = 57.21 kJ

Therefore, the answer is B) 57.2 kJ.

A Kilogram of Water (C = 4