Twenty grams of aluminum metal at 83.2 C were mixed with 49.3 g of water at 19.7 C. Assuming no heat loss, what was the final temperature of the Aluminum water metal? specific heat for Al= 0.215 specific heat for H2O=1.00

Question

Twenty grams of aluminum metal at 83.2 C were mixed with 49.3 g of water at 19.7 C. Assuming no heat loss, what was the final temperature of the Aluminum water metal? specific heat for Al= 0.215 specific heat for H2O=1.00

Answer 1

heat lost by Al + heat gained by water = 0

(mass Al x specific heat Al x (Tfinal-Tinitial) + (mass H2O x specific heat H2O x (Tfinal-Tinitial) = 0
Substitute and solve for Tf of the Al and H2O.

Answer 2

To find the final temperature of the aluminum-water mixture, we can apply the principle of conservation of energy. The heat lost by the aluminum (Q_al) will be equal to the heat gained by the water (Q_w):

Q_al = -Q_w

The heat lost by the aluminum can be calculated using the formula:

Q_al = m_al * c_al * ΔT_al

where:
m_al is the mass of aluminum (20 g),
c_al is the specific heat of aluminum (0.215 cal/g°C), and
ΔT_al is the change in temperature of aluminum (final temperature - initial temperature).

The heat gained by the water can be calculated using the formula:

Q_w = m_w * c_w * ΔT_w

where:
m_w is the mass of water (49.3 g),
c_w is the specific heat of water (1.00 cal/g°C), and
ΔT_w is the change in temperature of water (final temperature - initial temperature).

Since the aluminum and water reach the same final temperature, we can express ΔT_al and ΔT_w as ΔT (final temperature - initial temperature).
Thus, we have:

Q_al = -Q_w
m_al * c_al * ΔT = -m_w * c_w * ΔT

Given:
m_al = 20 g
c_al = 0.215 cal/g°C
m_w = 49.3 g
c_w = 1.00 cal/g°C

We can rearrange the equation to find ΔT:

m_al * c_al * ΔT = -m_w * c_w * ΔT
20 g * 0.215 cal/g°C * ΔT = -49.3 g * 1.00 cal/g°C * ΔT

Now, let's solve for ΔT:

20 g * 0.215 cal/g°C * ΔT = -49.3 g * 1.00 cal/g°C * ΔT
4.3 cal/°C * ΔT = -49.3 cal/°C * ΔT
4.3 = -49.3 / ΔT

To eliminate ΔT from the equation, we divide both sides by (-49.3):

4.3 / (-49.3) = ΔT / ΔT
-0.08734 = 1

Since -0.08734 does not equal 1, this means that ΔT (final temperature - initial temperature) cannot be determined. There is no final temperature solution without additional information as the equation does not balance.

Note: It is important to check your math and balance the equation before proceeding with the final calculation. Please double-check your data and calculations to ensure accuracy.