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Answer :
To achieve a final temperature of 37.1°C, you need to mix 108.1 mL of water at 64.3°C with 177 mL of water at 20.5°C.
To find the volume of water at 64.3°C that needs to be mixed with 177 mL of water at 20.5°C to achieve a final temperature of 37.1°C, we apply the principle of conservation of energy, assuming no heat is lost to the environment.
The specific heat of water is constant, and the heat lost by the hot water will equal the heat gained by the cold water:
- Heat lost by hot water = Heat gained by cold water
Let [tex]V_h[/tex] be the volume of the hot water:
- Mass of hot water ([tex]m_h[/tex]) = [tex]V_h[/tex] g
- Mass of cold water ([tex]m_c[/tex]) = 177 g
The specific heat capacity (c) of water is approximately 4.184 J/g°C. Using the heat transfer formula, we have:
- [tex]m_h \cdot c \cdot (T_{\text{initial, hot}} - T_{\text{final}}) = m_c \cdot c \cdot (T_{\text{final}} - T_{\text{initial, cold}})[/tex]
Substitute the known values:
- [tex]V_h \times 4.184 \times (64.3 - 37.1) &= 177 \times 4.184 \times (37.1 - 20.5) \\[/tex]
- [tex]V_h \times 4.184 \times 27.2 &= 177 \times 4.184 \times 16.6 \\[/tex]
- [tex]V_h \times 27.2 &= 177 \times 16.6 \\[/tex]
- [tex]V_h &= \frac{177 \times 16.6}{27.2} \\[/tex]
- [tex]V_h &= 108.1 \, \text{mL}[/tex]
Thus, you need 108.1 mL of water initially at 64.3°C to mix with 177 mL of water at 20.5°C to achieve a final temperature of 37.1°C.
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Rewritten by : Barada
The volume of water initially at 64.3ºC, needs to be mixed with 177 mL of water is 108 mL.
Density of water = 12/ mL
According to law of heat conservation = m ( h) × ep × Δt = m(e) ×ep × Δt
m(h) × [ 64.3 - 37 .1 ] = 177 × [ 37.1 - 20.5 ]
m( h ) × 27.2 = 177 × 16.6
m( h) = (177 × 16.6 )/ 27.2
= 108 mL
What is heat law of conservation?
According to the First Law of Thermodynamics, a system's total energy increase is proportional to the system's work and thermal energy. According to this, heat is an energy type that is subject to conservation, or the fact that it cannot be created or destroyed.
What is conservation significance?
The most obvious goal of conservation is to preserve biodiversity and conserve wildlife. Additionally, preserving wildlife for future generations ensures that the beloved animals we care about will not vanish from our memories. Additionally, we are able to maintain an ecosystem that is both functional and healthy.
Learn more about Heat law of conservation:
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