These are Thermodynamics questions:

Question

These are Thermodynamics questions:
There is a 7 kg piece of aluminum at 80°C placed in a 3 kg water at 20°C what is the final temperature?

There is a piece of aluminum at 90°C placed in 2 kg of water at 35°C how much energy is transferred if the final temperature is 45? What is the weight of the aluminum?

Answer 1

I will set these up for you, and you can work the math.

 

(1)

 

m₁ = mass of the Al = 7 kg
m₂ = mass of water = 3 kg
T₁ = initial temperature of the Al = 80°C
T₂ = initial temperature of the water = 20°C
c₁ = specific heat of Al (look it up in your physics or chemistry book)
c₂ = specific heat of water (look it up in your physics or chemistry book)
T = final temperature of system when equilibrium is reached = ?

 

Equilibrium condition:

 

m₁c₁(T₁ - T) = m₂c₂(T - T₂)

 

Everything in the equation is given to you or you can look it up in tables, except T.  Just do the algebra to solve for the unknown T in terms of the known quantities, and plug in the numbers.  Be careful with units.

 

(2)

 

m₁ = mass of the Al = ?
m₂ = mass of water = 2 kg
T₁ = initial temperature of the Al = 90°C
T₂ = initial temperature of the water = 35°C
c₁ = specific heat of Al (look it up in your physics or chemistry book)
c₂ = specific heat of water (look it up in your physics or chemistry book)
T = final temperature of system when equilibrium is reached = 45°C

Q = heat transfer into the water = ?

 

Q = m₂c₂(T - T₂) 

 

Plug in the numbers and get Q.

 

The equilibrium condition still applies.

 

m₁c₁(T₁ - T) = m₂c₂(T - T₂)

 

This time, you know everything (including T) except m₁.  Do the algebra to solve for m₁.  Again, be careful with units.