The specific heat of water is 4.2 kJ/kg$\degree$C. How long will it take for a 2-kW heating element to raise the temperature of 30 kg of water from 20$\degree$C to 80$\degree$C?
A) 6.3 min
B) 15 min
C) 63 min
D) 84 min

Question

Quizplus · Accepted Answer

The formula to calculate the amount of heat required to raise the temperature of a substance is:

Q = m * c * ΔT

where, 
Q = amount of heat required (in Joules)
m = mass of substance (in kg)
c = specific heat of substance (in J/kg°C)
ΔT = change in temperature (in °C)

Here, 
m = 30 kg 
c = 4.2 kJ/kg°C (convert to J/kg°C) 
ΔT = (80°C - 20°C) = 60°C

Substituting these values in the formula:

Q = 30 * 4.2 * 60,000 = 7,560,000 J

Now, we need to find how long a 2-kW heating element will take to provide this amount of heat.

Power (P) = 2 kW = 2,000 W 
Time (t) = ?

The formula to calculate the amount of energy provided by a power source in a given time is:

Energy (E) = Power (P) * Time (t)

We can rearrange this formula to find the time taken:

Time (t) = Energy (E) / Power (P)

Substituting the values:

t = 7,560,000 J / 2,000 W = 3,780 s = 63 min

Therefore, the answer is C) 63 min.

The Specific Heat of Water Is 4 °\degree° C How Long Will It Take for a 2-KW Heating

The Specific Heat of Water Is 4 $\degree$ C How Long Will It Take for a 2-KW Heating