Answer: The equilibrium temperature of the system is 29.9°C
Explanation:
When chilled glass is dropped in water, the amount of heat released by water will be equal to the amount of heat absorbed by glass.
[tex]Heat_{\text{absorbed}}=Heat_{\text{released}}[/tex]
The equation used to calculate heat released or absorbed follows:
[tex]Q=m\times c\times \Delta T=m\times c\times (T_{final}-T_{initial})[/tex]
[tex]m_1\times c_1\times (T_{final}-T_1)=-[m_2\times c_2\times (T_{final}-T_2)][/tex] ......(1)
where,
q = heat absorbed or released
[tex]m_1[/tex] = mass of glass = 32 g
[tex]m_2[/tex] = mass of water = 54 g
[tex]T_{final}[/tex] = final temperature = ? °C
[tex]T_1[/tex] = initial temperature of glass = 12°C
[tex]T_2[/tex] = initial temperature of water = 37°C
[tex]c_1[/tex] = specific heat of glass = 0.840 J/g°C
[tex]c_2[/tex] = specific heat of water= 4.186 J/g°C
Putting values in equation 1, we get:
[tex]32\times 0.840\times (T_{final}-12)=-[54\times 4.186\times (T_{final}-32)][/tex]
[tex]T_{final}=29.9^oC[/tex]
Hence, the equilibrium temperature of the system is 29.9°C
