d) How much 5°C cold water does she need to fill in the bathtub for the mixture to become 38°C? E) What does the third law of thermodynamics sound like?

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No heat losses exist in this task. Hampus is concerned about the expensive electricity price. Stingy as he is, he tells his daughter that she is not allowed to bathe in the bathtub. Assume that the water temperature entering the house is 5.0°C. For the bath to be pleasant, the bath water must be 38°C.

 

 

 

a) How much energy is needed to heat the water to 38°C in a bathtub of size 0.150 m³?

 

 

 

b) How long does it take for the water heater to heat 0.150 m³ of water from 5.0°C to 38°C if it has an output of 1.0kW and an efficiency of n = 0.80 ?

 

 

 

c) How much does a bath cost if the electricity price for 1 kWh is $5? Hampu's daughter does not care about the electricity price, so she pours a bath when Hampu is not at home. Unfortunately, the bath water is 45°C, so she adds cold water until the water is 38°C.

 

 

 

d) How much 5°C cold water does she need to fill in the bathtub for the mixture to become 38°C?

E) What does the third law of thermodynamics sound like?

 

 

 

Expert Solution
Step 1

If no heat is lost to the surroundings, the amount of heat acquired by the cold body equals the amount of heat lost by the hot body.

To find: 

  • How much 5°C cold water does she need to fill in the bathtub for the mixture to become 38°C?
  • What does the third law of thermodynamics sound like?

Given: 

  • Final temperature=380C
  • bathtub of size 0.150 m³
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