Question

A 37.5-g glass thermometer reads 24.1 ∘C before it is placed in 123 mL of water. When the water and thermometer come to equilibrium, the thermometer reads 41.8 ∘C. Ignore the mass of fluid inside the glass thermometer. The value of specific heat for water is 4186 J/kg⋅C∘, and for glass is 840 J/kg⋅C∘.

What was the original temperature of the water?

Express your answer using three significant figures.

Answer 1

Mass of glass thermometer = m_g = 37.5 g = 0.0375 kg

Volume of water = V = 123 mL = 123 x 10^-6 m³

Density of water = = 1000 kg/m³

Mass of water = m_w

m_w = V

m_w = (1000)(123 x 10^-6)

m_w = 0.123 kg

Initial temperature of glass thermometer = T₁ = 24.1 ^oC

Initial temperature of water = T₂

Final temperature of glass thermometer and water = T = 41.8 ^oC

Specific heat of water = C_w = 4186 J/(kg.^oC)

Specific heat of glass = C_g = 840 J/(kg.^oC)

The heat gained by the glass thermometer is equal to the heat lost by the water.

m_gC_g(T - T₁) = m_wC_w(T₂ - T)

(0.0375)(840)(41.8 - 24.1) = (0.123)(4186)(T₂ - 41.8)

T₂ - 41.8 = 1.083

T₂ = 42.883 ^oC

Original temperature of water = 42.883 ^oC