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Answer the following.(a) How much energy is necessary to heat 3.5 kg of water from room temperature (20°C) to its boiling point? (Assume no energy loss.)answer in:____ kcal(b) If electrical energy were used, how much would this cost at 13¢ per kWh?answer in:____ ¢



Answer :

Given:

Mass, m = 3.5 kg

Initial temperature, T1 = 20°C

Final temperature, T2 = Boiling point of water = 100° C

Part (a).

Let's find the amount of energy needed.

Apply the specific heat capacity formula:

[tex]\begin{gathered} Q=mc\Delta T \\ \\ Q=mc(T_2-T_1) \end{gathered}[/tex]

Where:

c is the specific heat capacity of water = 4.187 kJ/g °C

Thus, we have:

[tex]\begin{gathered} Q=3.5*4.187*(100-20) \\ \\ Q=3.5*4.187*80 \\ \\ Q=1172.36\text{ kJ} \end{gathered}[/tex]

Where:

1 kJ = 0.239 kCal

1172.36 kJ = 1172.36 x 0.239 = 280.19 kCal

Therefore, the heat needed is 280.19 kCal.

Part B.

Given:

Cost = 13¢ per kWh

Where:

1 kCal = 0.00116 kWh

280.19 x 0.00116 = 0.327 kWh

Since the charge for is 13 ¢ per kWh, we have:

13 x 0.327 = 4.251 ¢.

Therefore, the cost, if electrical energy were used, will be 4.251 ¢

ANSWER:

• (a). 280.19 kCal

• (b)., ,4.251 ¢.

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