A block of aluminum with a mass of 2.6 kg is at 13C and comes in contact with a hot block of copper with a mass of 10.2 kg at 93C. What is the equilibrium temperature in Celsius degrees?

caluminum = 0.22 kcal/kgC
ccopper = 0.093 kcal/kgC

Heat gained by aluminum equals heat lost by copper. Let T be the final equilibrium temperature of both.

The heat gain of each metal is
Q = M*C*(T2 - T1). It heat is lost, that number is negative

2.6*0.22*(T-13) = 10.2*0.093*(93-T)

Solve for T.

0.572T - 7.436 = 88.22 - 0.9486 T
1.5206 T = 95.65
T = 63 C

why is the heat lost by the metal sample (Ql)equal to he heat gained by the water in the calorimeter (QG)?

To find the equilibrium temperature in Celsius degrees, we can use the principle of energy conservation.

The amount of heat lost by the hot copper block will be equal to the amount of heat gained by the cold aluminum block in order for them to reach the same temperature.

The heat lost by the copper block can be calculated using the formula:

Q = mcΔT

Where,
Q = heat lost
m = mass of copper block
c = specific heat capacity of copper
ΔT = change in temperature (final temperature - initial temperature)

Substituting the given values:

Q(copper) = 10.2 kg * 0.093 kcal/kg°C * (T - 93°C)

The heat gained by the aluminum block can be calculated using the same formula:

Q = mcΔT

Where,
Q = heat gained
m = mass of aluminum block
c = specific heat capacity of aluminum
ΔT = change in temperature (final temperature - initial temperature)

Substituting the given values:

Q(aluminum) = 2.6 kg * 0.22 kcal/kg°C * (T - 13°C)

Since the heat lost by the copper block is equal to the heat gained by the aluminum block, we can set the two equations equal to each other:

10.2 kg * 0.093 kcal/kg°C * (T - 93°C) = 2.6 kg * 0.22 kcal/kg°C * (T - 13°C)

Now we can solve for T, the equilibrium temperature:

10.2 * 0.093 * (T - 93) = 2.6 * 0.22 * (T - 13)

To simplify the equation, you can first distribute the terms:

0.9486T - 876.204 = 0.572T - 7.48

Combine like terms:

0.9486T - 0.572T = 876.204 - 7.48

0.3766T = 868.724

Now, divide both sides by 0.3766:

T = 868.724 / 0.3766

T ≈ 2305.68

Therefore, the equilibrium temperature is approximately 2305.68°C.