Question

Suppose 0.48 g of water at 25°C condenses on the surface of a 55 g block of aluminum that is initially at 25°C. If the heat released during the condensation goes only toward heating the metal, what is the final temperature (in °C) of the metal block? (Specific heat of Al: 0.903 J/g°C)

A) 0°C
B) 25°C
C) 50°C
D) 75°C

Answer 1

The final temperature of the aluminum block is approximately 75°C.

Step-by-step explanation:

In this problem, we need to find the final temperature of the aluminum block after water condenses on its surface. We can use the equation:

Q = mcΔT

where Q is the heat released, m is the mass, c is the specific heat, and ΔT is the change in temperature.

First, we calculate the heat released by the water:

Q_water = mcΔT = (0.48 g)(4.18 J/g °C)(25 - 0) = 49.92 J

Since the heat released goes only toward heating the aluminum block, we can set up an equation to find the final temperature:

Q_aluminum = mcΔT

49.92 J = (55 g)(0.903 J/g °C)(T - 25)

Solving for T gives us:

T = 49.92 J / (55 g * 0.903 J/g °C) + 25 °C

T ≈ 75°C

Therefore, the final temperature of the aluminum block is approximately 75°C.