A new metal alloy is found to have a specific heat capacity of 0.260 J / (g⋅∘C). First, 47 g of the new alloy is heated to 180. ∘C. Then, it is placed in an ideal constant-pressure calorimeter containing 110. g of water (Cs, water=4.184 J / (g⋅∘C)) at an initial temperature of 20.0 ∘C. What will the final temperature of the mixture be after it attains thermal equilibrium?

The final temperature, at the equilibrium is 24.14 °C

Explanation:

Step 1: Data given

specific heat capacity of alloy = 0.260 J / (g°C)

MAss of alloy = 47 grams

Mass of water = 110 grams

Specific heat of water = 4.184 J/g°C

Initial temperature of water = 20.0 °C

Initial temperature of alloy = 180.0 °C

Step 2: Calculate the final temperature at equilibrium

Heat lost = heat gained

Qlost = - Qgained

Q (alloy) = - Q (water)

Q=m*c*ΔT

Q = m (alloy) * c (alloy) * ΔT (alloy) = - m (water) * c (water) * ΔT (water)

⇒with m (alloy) = the mass of alloy = 47.0 grams

⇒with c (alloy) = the specific heat of alloy = 0.260 J/g°C

⇒with ΔT (alloy) = the change of temperature = T2 - T1 = T2 - 180 °C

⇒with m (water) = the mass of water = 110 grams

⇒with c (water) = the specific heat of water = 4.184 J/g°C

⇒with ΔT (water) = the change of temperature = T2 - 20.0°C

47.0*0.260 * (T2 - 180.0) = - 110 * 4.184 * (T2 - 20.0)

12.22 (T2-180.0) = - 460.24 (T2 - 20)

12.22T2 - 2199.6 = - 460.24T2 + 9204.8

472.46T2 = 11404.4

T2 = 24.14 °C

The final temperature, at the equilibrium is 24.14 °C