A block of aluminum of massm1 at temperature T1 and a block ofcopper of mass m2

Question

A block of aluminum of massm1 at temperature T1 and a block ofcopper of mass m2 at temperature T2 are brought into contact in aninsulated container. Derive expressions for the finaltemperature and the netentropy change of the system, the surroundings and the universe.Perform a numericalcalculation for T1 = 500 C,T2 = 100 C, m1 = 5kg, m2 = 1 kg. Use thespecific heat capacity values at the intermediate temperature of300°C, and assume thatthese are independent of temperature over the given temperaturerange.

Explanation / Answer

Given data T1 = 500 C, T2 = 100 C,
   m1= 5kg, m2 = 1 kg. Specific heatcapacity = s Let us take finaltemperature = Tf Heat lost by hotbody = m1 s(T1 -Tf ) Heat gained bycold body = m2 s (Tf -T2) The container isinsulated Heatlost by hot body = Heat gained by coldbody          m1 s (T1 -Tf ) =  m2 s (Tf -T2)           m1 (T1 -Tf ) =  m2 (Tf -T2)     (5kg)(500 - Tf ) = (1kg)(Tf -100)                          Tf = 433.33 0C     Specific heatcapacity = s Let us take finaltemperature = Tf Heat lost by hotbody = m1 s(T1 -Tf ) Heat gained bycold body = m2 s (Tf -T2) The container isinsulated Heatlost by hot body = Heat gained by coldbody          m1 s (T1 -Tf ) =  m2 s (Tf -T2)           m1 (T1 -Tf ) =  m2 (Tf -T2)     (5kg)(500 - Tf ) = (1kg)(Tf -100)                          Tf = 433.33 0C    

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