Calculating initial temperature of a sample

Question

A 50.8g sample of quartz, which has a specific heat capacity of 0.730 J⋅g^-1⋅°C^-1, is put into a calorimeter that contains 200.0g of water. The temperature of the water starts off at 15.0°C. When the temperature of the water stops changing it's 18.1°C. The pressure remains constant at 1atm. Calculate the initial temperature of the quartz sample. Be sure your answer is rounded to the correct number of significant digits.

Answer 1

Using Q = mC_pΔT, calculate the heat required to raise the temperature of the water. In this equation "Q" is the heat energy required (or lost) when an item of mass "m", having a specific heat capacity of C_p, goes through a temperature change ΔT.

For this water bath, use m = 200.0 g, C_p = 4.186 J/(g°C), and ΔT = 18.1 - 15 = 3.1 °C

Q = (200.0)(4.186)(3.1) = 2595.32 joules

The heat gained by the water is the same as the heat lost by the quartz except, since the quartz lost heat, the value is negative. Use the same equation to calculate the initial temp of the quartz:

Q = mC_pΔT = mC_p(T_f - T_i) where T_f = final temp and T_i is the initial temp (what we are looking for)

-2595.32 = (50.8)(0.730)(18.1 - T_i)

-2595.32 = (37.084)(18.1 - T_i)

(-2595.32)/(37.084) = 18.1 - T_i

-69.985 = 18.1 - T_i

T_i = 69.985 + 18.1

T_i = 88.1 °C