Three samples of different substances—A, B

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

Problem

Three samples of different substances—A, B, and C—are simultaneously placed into an ideal insulated container and allowed to reach a common equilibrium temperature. The samples have the following properties: • Mass of A: mAm_A; specific heat of A: cAc_A; initial temperature of A: TAT_A • Mass of B: mBm_B; specific heat of B: cBc_B; initial temperature of B: TBT_B • Mass of C: mCm_C; specific heat of C: cCc_C; initial temperature of C: TCT_C No energy is exchanged with the surroundings, and the container itself has negligible heat capacity. (1) Derive a symbolic expression for the common equilibrium temperature TfT_f in terms of the given variables. Show each step of your algebraic reasoning without substituting numerical values. (2) Use your derived expression to compute TfT_f for the following numerical values: mA=0.200 kgm_A = 0.200\,\text{kg}, cA=1200 J kg−1 K−1c_A = 1200\,\text{J}\,\text{kg}^{-1}\,\text{K}^{-1}, TA=350 KT_A = 350\,\text{K}; mB=0.150 kgm_B = 0.150\,\text{kg}, cB=900 J kg−1 K−1c_B = 900\,\text{J}\,\text{kg}^{-1}\,\text{K}^{-1}, TB=280 KT_B = 280\,\text{K}; and mC=0.300 kgm_C = 0.300\,\text{kg}, cC=4200 J kg−1 K−1c_C = 4200\,\text{J}\,\text{kg}^{-1}\,\text{K}^{-1}, TC=295 KT_C = 295\,\text{K}. Provide the final temperature with a suitable unit and the appropriate number of significant figures.

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