You are in the research lab and someone accidentally cough c

You are in the research lab and someone \"accidentally\" (cough, cough...lab safety...cough, cough) drops 11.0 g of aluminum at 200^degreeC and 20.0 g of copper into 55.0 cm^3 of ethyl alcohol at 15.0^degreeC. The temperature quickly rises to 23.0^degreeC. What was the initial temperature of the copper in ^degreeC?

Solution

Ethyl alcohol density = 0.789 g/cm³

Ethyl alcohol mass = 55x0.789 = 43.39 gm

Specific heat of Aluminium = 0.900J/gm K

Specific heat of Copper = 0.386J/gm K

Specific heat of Ethyl alcohol = 2.4J/gm K

Assume that cuopper initai temperature was T_o

So Heat loss by copper and aluminum should be equivalent to heat gain by ethyl alcohol

m_ethylS_ethylT_ethyl = m_alS_alT_al +m_cuS_cuT_cu

43.39x2.4x(23-15)=11x0.9x(200-23)+20x0.386(T_o-23)

T_o = -96.07°C