A well-insulated calorimeter of negligible heat capacity contains two equal masses of…

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A well-insulated calorimeter of negligible heat capacity contains two equal masses

m=0.200\,\text{kg}

of water. Sample 1 is initially at

90.0^{\circ}\text{C}

, and Sample 2 is at

10.0^{\circ}\text{C}

. When the samples are mixed, a narrow vent in the calorimeter lid allows a small but measurable energy leak to the environment. After

60\,\text{s}

, thermal equilibrium is reached at a measured temperature of

48.0^{\circ}\text{C}

. The specific heat capacity of liquid water is

c_w=4186\,\text{J}\,\text{kg}^{-1}\,\text{K}^{-1}

. (a) Assuming the calorimeter were perfectly isolated, calculate the equilibrium temperature

T_{\text{ideal}}

that would be expected. (b) Using the measured final temperature, determine the total amount of energy

Q_{\text{leak}}

that left the calorimeter during the

60\,\text{s}

mixing interval. (c) Compute the average rate (power) at which energy escaped through the vent. (d) Discuss whether modeling the calorimeter as an isolated system would introduce a significant or negligible error for typical laboratory purposes, citing the magnitudes you obtained.

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