Beryllium has roughly one-half the specific heat of water (H2O). Rank the quantities of energy input required to produce the following changes from the largest to the smallest. In your ranking, note any cases of equality, (a) raising the temperature of 1 kg of H2O from 20°C to 26ºC (b) raising the temperature of 2 kg of H2O from 20ºC to 23°C (c) raising the temperature of 2 kg of H2O from 1ºC to 4°C (d) raising the temperature of 2 kg of beryllium from — 1°C to 2°C (e) raising the temperature of 2 kg of H2O from -1°C to 2°C
The rank from the largest to smallest according to the required energy input.
Answer to Problem 20.8OQ
The rank from the largest to smallest according to the required energy input is
Explanation of Solution
Given info: The specific heat of the Beryllium is one half of the specific heat of the water.
Write the expression to relate the specific heat of the Beryllium to the specific heat of the water.
Here,
The specific heat of water is
Substitute
Thus, the specific heat of the Beryllium is
The change in the temperature is calculated as,
Here,
The amount of energy required for the rise in temperature of water is,
Here,
Substitute
For case (a),
The mass of
Substitute
Thus, the energy required in case (a) is
For case (b),
The mass of
Substitute
Thus, the energy required in case (b) is
For case (c),
The mass of
Substitute
Thus, the energy required in case (c) is
For case (d),
The mass of beryllium is
Substitute
Thus, the energy required in case (d) is
For case (e),
The mass of
For the temperature in negative
Substitute
From temperature
Here,
The latent heat of fusion of ice is
Substitute
From
Substitute
The total energy required in case (e) is,
Substitute
Thus, the energy required in case (e) is
Conclusion:
Therefore, the rank from the largest to smallest according to the required energy input is
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Chapter 20 Solutions
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