A kettle is full of water. The kettle uses 497,000 J of energy to raise the temperature of the water from 20°C to 100°C. Show that the mass of water in the kettle is approximately... A kettle is full of water. The kettle uses 497,000 J of energy to raise the temperature of the water from 20°C to 100°C. Show that the mass of water in the kettle is approximately 1.5 kg. Use the equation Q = mcΔT. Specific heat capacity of water = 4200 J kg⁻¹ °C⁻¹. Show your working.
Understand the Problem
The question is asking to calculate the mass of water in a kettle based on the energy used to heat it from 20°C to 100°C using the formula Q = mcΔT. The provided data includes the energy used (497,000 J), the specific heat capacity of water (4200 J kg⁻¹ °C⁻¹), and the temperature change (ΔT).
Answer
The mass of water in the kettle is approximately $1.5 \, kg$.
Answer for screen readers
The mass of water in the kettle is approximately $1.5 , kg$.
Steps to Solve
- Identify the formula We will use the formula for heat transfer: $$ Q = mc\Delta T $$ where:
- ( Q ) is the energy in joules (J)
- ( m ) is the mass in kilograms (kg)
- ( c ) is the specific heat capacity (J kg⁻¹ °C⁻¹)
- ( \Delta T ) is the change in temperature (°C)
- Determine the values needed We have the following values from the problem:
- Energy ( Q = 497,000 , J )
- Specific heat capacity of water ( c = 4200 , J , kg^{-1} °C^{-1} )
- Initial temperature ( T_i = 20°C )
- Final temperature ( T_f = 100°C )
- The change in temperature ( \Delta T = T_f - T_i = 100 - 20 = 80°C )
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Rearrange the formula to solve for mass (m) To find the mass of water, rearrange the equation to isolate ( m ): $$ m = \frac{Q}{c\Delta T} $$
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Substitute in the known values Substituting the known values into the rearranged equation: $$ m = \frac{497,000}{4200 \times 80} $$
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Calculate the denominator Calculating ( c\Delta T ): $$ 4200 \times 80 = 336,000 $$
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Calculate the mass Now substitute that back into the equation to find ( m ): $$ m = \frac{497,000}{336,000} $$
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Perform the division Now we calculate the final value: $$ m \approx 1.477 , kg $$
We can round this to approximately ( 1.5 , kg ) for simplicity.
The mass of water in the kettle is approximately $1.5 , kg$.
More Information
This calculation illustrates how much energy is required to heat water. It also emphasizes the relationship between energy, mass, and temperature change in heating processes.
Tips
- Forgetting to convert the temperature change to the correct unit (it should be in °C, which is already the case here).
- Mixing up the values for ( Q ), ( c ), and ( \Delta T ) when substituting into the formula.
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