Question

Calculate the specific heat of aluminum in J/K-g if the changes in temperature of a 7.2500 g of aluminum (∆T Al) is 172.5 °C; and the changes in temperature of 98.8 g of water (∆T water) in the calorimeter is 2.52 °C. (Water has specific heat of 4.184 J/K.g)

a) 0.896 J/K-g
b) 0.742 J/K-g
c) 0.425 J/K-g
d) 0.621 J/K-g

Answer 1

The specific heat of aluminum is calculated using calorimeter principles, equating the heat lost by aluminum to the heat gained by water. After setting up the equations and solving for the specific heat of aluminum (cAl), the value is found to be 0.832 J/g°C.

Step-by-step explanation:

To calculate the specific heat of aluminum, we need to use the principle of calorimeter, where the heat lost by aluminum (QAl) is equal to the heat gained by water (Qwater). Using the formula Q = mcΔT, where m is mass, c is specific heat, and ΔT is the change in temperature, we can set up the equation based on the principle that QAl = -Qwater (the negative sign indicates heat lost by aluminum is gained by water).

For water: Qwater = mwater x cwater x ΔTwater = 98.8 g x 4.184 J/g°C x 2.52°C = 1041.715 J

For aluminum: QAl = mAl x cAl x ΔTAl = 7.2500 g x cAl x 172.5°C

Setting QAl = -Qwater and solving for cAl gives:

7.2500 g x cAl x 172.5°C = -1041.715 J

cAl = -1041.715 J / (7.2500 g x 172.5°C)

cAl = -1041.715 J / (1250.625 g°C) = -0.832 J/g°C

The negative sign indicates the direction of heat flow, not the actual specific heat value, so we take the absolute value:

cAl = 0.832 J/g°C