Question

The coffee machine heats water from 20 °C to 90 °C.

Answer 1

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 = $T_1=20\°C$

Final temperature of water = $T_2=90\°C$

Power of coffee machine = $P=2.53\ KW$

Specific heat capacity of water = $c=4200\ J/kg\°C.$

Time for which water is heated = $t=14\ s$

Mass of water = m = ?

Power is defined as work done in unit time. Let the heat energy be Q. Power (P) is defined as $P = \frac{Q}{t}$ where t denotes the time for which energy is supplied. Q can be rewritten as:

$Q = P\times t = 2.53\times 14 = 35.42\ KJ$

$Q = 35.42\times 1000\ Joules = 35420\ J$......................(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) = $T_2-T_1$.......................(3)

From (1) and (3), solving equation (2) for m;

Q = m×c×Δt

$Q=m\times c\times (T_2-T_1)\\\\m=\frac{Q}{c\times (T_2-T_1)} = \frac{35420}{4200\times (90-20)}= \frac{35420}{294000} = 0.1204\ kg$

The mass of water that the coffee machine can heat in 14 seconds is equal to 0.1204 kg.