A 300-g glass thermometer initially at 25°C is put into 200 cm³ of hot water at 95°C. Find the final temperature (in °C) of the thermometer, assuming no heat flows to the surroundings. (The specific heat of glass is 0.2 cal/g⋅°C.) A) 52 B) 68 C) 89 D) 79 E) 36

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Quizplus · Accepted Answer

To find the final temperature, we use the principle of conservation of energy, where the heat lost by the hot water equals the heat gained by the thermometer. The formula for heat is $Q = mc\Delta T$, where $m$ is mass, $c$ is specific heat, and $\Delta T$ is the change in temperature. Let $T_f$ be the final temperature.For the thermometer: $Q_{glass} = m_{glass}c_{glass}(T_f - 25)$For the water: $Q_{water} = m_{water}c_{water}(95 - T_f)$Since no heat is lost to the surroundings, $Q_{glass} = Q_{water}$.Given $m_{glass} = 300g$, $c_{glass} = 0.2 cal/g°C$, $m_{water} = 200g$ (assuming the density of water is $1g/cm^3$), and $c_{water} = 1 cal/g°C$ (specific heat of water),$300 \times 0.2 \times (T_f - 25) = 200 \times 1 \times (95 - T_f)$Solving for $T_f$ gives a final temperature of approximately 79°C.

A 300-G Glass Thermometer Initially at 25°C Is Put into 200