Question

The value of specific heat for copper is 390 J/kg?C?, for aluminun is 900 J/kg?C?, and for water is 4186 J/kg?C?. What will be the equilibrium temperature when a 215 g block of copper at 255 ?C is placed in a 155 g aluminum calorimeter cup containing 875 g of water at 16.0 ?C?

Answer 1

Suppose the final temperature is T.

Now Using energy conservation:

Heat gained by water and calorimeter = Heat released by copper

Q1 + Q2 = Q3

m1*C1*dT1 + m2*C2*dT2 = m3*C3*dT3

dT1 = Tf - Ti = T - 16

dT2 = T - 16

dT3 = 255 - T

m1 = mass of water = 0.875 kg

m2 = mass of calorimeter = 0.155 kg

m3 = mass of copper = 0.215 kg

Now using given values:

0.875*4186*(T - 16) + 0.155*900*(T - 16) = 0.215*390*(255 - T)

Now Solving above equation

T = (0.875*4186*16 + 0.155*900*16 + 0.215*390*255)/(0.875*4186 + 0.155*900 + 0.215*255)

T = 21.32 C

Please Upvote.

OR you can use this formula directly next time

T = (m1c1T1 + m2c2T2 + m3c3T3)/(m1c1 + m2c2 + m3c3)