The power of the kettle was 2.6 kW. The kettle took 120 seconds to heat 0.80 kg of water from 18 °C to 100 °C. Calculate the specific heat capacity of water using this information. Give your answer to 2 significant figures.

Convert power to watts: P = 2.6 kW = 2600 W .
Calculate total energy: E = P × t = 2600 W × 120 s = 312000 J .
Calculate the change in temperature: Δ T = 100 °C − 18 °C = 82 °C .
Calculate specific heat capacity and round to 2 significant figures: c = 0.80 kg × 82 °C 312000 J ​ ≈ 4800 kg ⋅ °C J ​ ​ .

Explanation

Problem Overview We are given the power of a kettle, the time it takes to heat a certain mass of water from an initial temperature to a final temperature. Our goal is to calculate the specific heat capacity of water using this information, rounded to 2 significant figures.

Convert Power to Watts First, let's convert the power from kilowatts (kW) to watts (W). We know that 1 kW = 1000 W, so: P = 2.6 kW = 2.6 × 1000 W = 2600 W

Calculate Total Energy Next, we calculate the total energy supplied by the kettle. Energy (E) is equal to power (P) multiplied by time (t): E = P × t = 2600 W × 120 s = 312000 J

Calculate Temperature Change Now, let's calculate the change in temperature ( Δ T ): Δ T = T final ​ − T initial ​ = 100 °C − 18 °C = 82 °C

State Heat Energy Formula We use the formula for heat energy: E = m × c × Δ T Where:



E is the energy in joules (J)
m is the mass in kilograms (kg)
c is the specific heat capacity in J/(kg·°C)
Δ T is the change in temperature in °C


Rearrange Formula for Specific Heat Capacity We need to rearrange the formula to solve for the specific heat capacity ( c ): c = m × Δ T E ​

Substitute Values and Calculate Now, we substitute the values into the equation: c = 0.80 kg × 82 °C 312000 J ​ = 0.80 × 82 312000 ​ kg ⋅ °C J ​ = 4756.09756 kg ⋅ °C J ​

Round to Significant Figures Finally, we round the answer to 2 significant figures. The calculated value is approximately 4756.10 J/(kg·°C). Rounding this to two significant figures gives us 4800 J/(kg·°C).

Final Answer Therefore, the specific heat capacity of water, rounded to 2 significant figures, is: 4800 kg ⋅ °C J ​ ​


Examples
Understanding specific heat capacity is crucial in many real-world applications. For instance, when designing cooling systems for engines, engineers need to know how much energy water can absorb before it boils. Similarly, in cooking, the high specific heat capacity of water allows it to distribute heat evenly, preventing food from burning easily. This concept is also vital in climate science, where the specific heat capacity of oceans influences global temperature regulation.

Answered by GinnyAnswer | 2025-07-04

To find the specific heat capacity of water, we calculated the total energy supplied by the kettle, the change in temperature, and then used the formula relating these values. After substituting the values into the formula for specific heat capacity, we found the answer to be approximately 4800 J/(kg·°C) rounded to two significant figures. Therefore, the specific heat capacity of water is 4800 J/(kg·°C).
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Answered by Anonymous | 2025-07-06