Respuesta :
Answer:
72.72 °C
Explanation:
[tex]m_g[/tex] = Mass of glass = 300 g
[tex]T_g[/tex] = Temperature of glass = 24 °C
[tex]T_w[/tex] = Temperature of water = 91 °C
[tex]m_w[/tex] = Mass of water = [tex]\rho v=1\ g/cm^3\times 160=160\ g[/tex]
[tex]T_f[/tex] = Final temperature of the thermometer
[tex]c_g[/tex] = Specific heat of glass = 0.2 cal/g°C
[tex]c_w[/tex] = Specific heat of water = 1 cal/g°C
In the case of a simple calorimetry
[tex]Q_g=m_gc_g(T_f-T_g)[/tex]
[tex]Q_w=m_wc_w(T_f-T_w)[/tex]
Heat flow is 0
[tex]Q_g+Q_w=0\\\Rightarrow m_gc_g(T_f-T_g)+m_wc_w(T_f-T_w)=0\\\Rightarrow T_f=\frac{m_gc_gT_g+m_wc_wT_w}{m_gc_g+m_wc_w}\\\Rightarrow T_f=\frac{300\times 0.2\times 24+160\times 1\times 91}{300\times 0.2+160\times 1}\\\Rightarrow T_f=72.72^{\circ}[/tex]
The final temperature of the thermometer is 72.72 °C
The final temperature of the the glass thermometer initially at 24 °C is put into 160 cm³ of hot water at 91 °C is 72.72 °C
How to determine the final temperature
We can obtain the final temperature of the thermometer by calculating the equilibrium temperature. This can be obtained as follow:
- Mass thermometer (M) = 300 g
- Specific heat capacity of thermometer (C) = 0.2 cal/gºC
- Temperature of thermometer (T) = 24 °C
- Mass of water (Mᵥᵥ) = 160 g
- Temperature of water (Tᵥᵥ) = 91 °C
- Specific heat capacity of the water (Cᵥᵥ) = 1 cal/gºC
- Equilibrium temperature (Tₑ) =?
Heat gained = Heat loss
MC(Tₑ – T) = MᵥᵥC(Tᵥᵥ – Tₑ)
300 × 0.2 (Tₑ – 24) = 160 × 1 (91 – Tₑ)
60(Tₑ – 24) = 160(91 – Tₑ)
Clear bracket
60Tₑ – 1440 = 14560 – 160Tₑ
Collect like terms
60Tₑ + 160Tₑ = 14560 + 1440
220Tₑ = 16000
Divide both side by 220
Tₑ = 16000 / 220
Tₑ = 72.72 °C
Therefore, the final temperature of the thermometer is 72.72 °C
Learn more about heat transfer:
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