Two liquids, X and Y

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Thermodynamics · Thermodynamics

Problem

Two liquids, X and Y, are to be mixed in an insulated steel calorimeter whose heat capacity is not negligible. Relevant data are given below. • Mass of liquid X:

0.150\,\text{kg}

• Initial temperature of liquid X:

90^{\circ}\text{C}

• Specific heat of liquid X:

3.5\times10^{3}\,\text{J}\,\text{kg}^{-1}\,\text{K}^{-1}

• Mass of liquid Y:

0.250\,\text{kg}

• Initial temperature of liquid Y:

20^{\circ}\text{C}

• Specific heat of liquid Y:

4.0\times10^{3}\,\text{J}\,\text{kg}^{-1}\,\text{K}^{-1}

• Heat capacity of the steel calorimeter cup and lid combined:

180\,\text{J}\,\text{K}^{-1}

After the liquids are poured together and the lid is closed, the system is allowed to come to equilibrium. A brief measurement indicates that

5.0\%

of the total energy exchanged between the liquids is lost to the surrounding air before equilibrium is reached. (1) Ignoring the stated

5.0\%

energy loss, calculate the equilibrium temperature the system would reach. Include the calorimeter cup in your calculation. (2) Taking the

5.0\%

energy loss into account, determine the actual equilibrium temperature reached by the system. Clearly outline how you incorporate the loss into your calculation. (3) Discuss, in one or two clear sentences, how neglecting the calorimeter’s heat capacity would affect the calculated equilibrium temperature in part (a). Specify whether the temperature would be overestimated or underestimated and briefly state why.

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