Respuesta :
The mass of water that the coffee machine can heat in 14 seconds is equal to 0.1204 kg.
Explanation:
Given:
Initial temperature of water = [tex]T_1=20\°C[/tex]
Final temperature of water = [tex]T_2=90\°C[/tex]
Power of coffee machine = [tex]P=2.53\ KW[/tex]
Specific heat capacity of water = [tex]c=4200\ J/kg\°C.[/tex]
Time for which water is heated = [tex]t=14\ s[/tex]
Mass of water = m = ?
Power is defined as work done in unit time. Let the heat energy be Q. Power (P) is defined as [tex]P = \frac{Q}{t}[/tex] where t denotes the time for which energy is supplied. Q can be rewritten as:
[tex]Q = P\times t = 2.53\times 14 = 35.42\ KJ[/tex]
[tex]Q = 35.42\times 1000\ Joules = 35420\ J[/tex]......................(1)
Formula for Heat energy is given by
Q = m×c×Δt ........................................(2)
where:
Q = Heat energy (in J)
m = mass of the substance being heated in grams(kg)
c = the specific heat of the substance in J/(kg.°C)
Δt = Change in temperature (in °C)
Δt = (Final temperature - Initial temperature) = [tex]T_2-T_1[/tex].......................(3)
From (1) and (3), solving equation (2) for m;
Q = m×c×Δt
[tex]Q=m\times c\times (T_2-T_1)\\\\m=\frac{Q}{c\times (T_2-T_1)} = \frac{35420}{4200\times (90-20)}= \frac{35420}{294000} = 0.1204\ kg[/tex]
The mass of water that the coffee machine can heat in 14 seconds is equal to 0.1204 kg.
