Question

If 50.0 g of an unknown liquid is heated to 95°C and mixed with 50 g of water at 21°C, what is the final temperature of the mixture?

a) 70°C
b) 80°C
c) 90°C
d) 95°C

Answer 1

The final temperature of the mixture, given that the specific heat capacity of the unknown liquid is 8.2 J/g°C, is 70 °C (option A)

How to calculate the final temperature of mixture?

The final temperature of the mixture will be the equilibrium temperature attained by the mixture of the two liquids.

Now, we shall calculate the equilibrium temperature in order to ascertain the final temperature. Details is shown below:

• Mass of unknown liquid (M) = 5 0g
• Initial temperature of unknown liquid (T) = 95 °C
• Specific heat capacity of unknown liquid (C) = 8.2 J/g°C
• Mass of water (Mᵥᵥ) = 50 g
• Initial temperature of water (Tᵥᵥ) = 21 °C
• Specific heat capacity of water (Cᵥᵥ) = 4.184 J/g°C
• Equilibrium temperature (Tₑ) =?

Heat evolved by unknown liquid = Head absorbed by water

`MC(T\ -\ T_e) = M_wC_w(T_e\ -\ T_w)\\\\50\ *\ 8.2(95\ -\ T_e) = 50\ *\ 4.184(T_e\ -\ 21)\\\\`

`38950\ -\ 410T_e = 209.2T_e\ -\ 4393.2\\\\Collect\ like\ terms\\\\38950\ +\ 4393.2 = 209.2T_e\ +\ 410T_e\\\\`

`43343.2 = 619.2T_e\\\\Divide\ both\ side\ by\ 619.2\\\\T_e = (43343.2)/(619.2) \\\\T_e \approx 70\ \textdegree C`

Now that we know that the equilibrium temperature is 70 °C. Thus, we can conclude that the final temperature of the mixture is 70 °C

Therefore, the correct answer is option A.

Complete question:

If 50.0 g of an unknown liquid is heated to 95°C and mixed with 50 g of water at 21°C, what is the final temperature of the mixture? [specific heat capacity of unknown liquid = 8.2 J/g°c]

a) 70°C

b) 80°C

c) 90°C

d) 95°C