Question

Answer the following.(a) How much energy is necessary to heat 3.0 kg of water from room temperature (20°C) to its boiling point? (Assume noenergy loss.) answer must be in kcal(b) If electrical energy were used, how much would this cost at 27¢ per kWh? Answer must be in ¢

Answer 1

Given:

Mass of water, m = 3.0 kg

Room temperature, T1 = 20°C

Let's find the amount of energy necessary to heat the water from 20°C to its boiling point.

Where:

Boiling Point of water, T2 = 100 °C

Apply the formula:

`\begin{gathered} H=mc\Delta T \\ \\ H=mc(T_2-T_1) \end{gathered}`

Where:

• H is the required energy

,

• m is the mass

,

• c is the specific heat capacity of water = 1.0 kcal/kg. °C

,

• T2 is the final temperature = 100 °C

,

• T1 = 20°C

Thus, we have:

`\begin{gathered} H=3.0*1.0*(100-20) \\ \\ H=3.0*1.0*80 \\ \\ H=240\text{ kcal} \end{gathered}`

Therefore, the required energy is 240 kcal.

• (b). If electrical energy were used, how much would this cost at 27¢ per kWh?

Where:

1 kcal = 0.00116 kWh

To find the cost at 27¢ per kWh, we have:

`240\text{ kcal}*\frac{0.00116\text{ kWh}}{kcal}*\frac{27¢}{1\text{ kwh}}=¢7.52`

Therefore, the cost will be 7.52¢

ANSWER:

• (a). 240 kcal

• (b). 7.52,¢