 # Thermal Energy Gain and Loss

When 2 objects/substances are in thermal contact, there will be a net flow of thermal energy from the object/substance with a higher temperature to the object/substance with lower temperature. If we assume there is no thermal energy loss to the surrounding

Thermal energy loss = Thermal energy gain Example 1:

A 0.5 kg block of aluminium at a temperature of 100 °C is placed in 1.0 kg of water at 20 °C. Assuming that no thermal energy is lost to the surroundings, what will be the final temperature of the aluminium and water when they come to the same temperature? [The specific heat capacity of water is 4200 Jkg-1K-1 and The specific heat capacity of aluminium is 900 Jkg-1K-1]

Let’s say the final temperature for both aluminium block and water = θ

For aluminium,
m1 = 0.5 kg
c1 = 900 Jkg-1K-1
∆θ1 = 100 °C – θ

For water,
m2 = 1.0kg
c2 = 4200 Jkg-1K-1
∆θ2 = θ – 20 °C Example 2:
What will be the final temperature if 50 g of water at 0 °C is added to 250 g of water at 90 °C?

For water at 90 °C,
m1 = 250g
c1 = c2 = c
∆θ1 = 90 °C – θ

For water at 0 °C,
m2 = 50g
∆θ2 = θ – 0 °C = θ Example 3:
How much water at 10 °C is needed to cool 500 g of water at 90 °C down to 30 °C? 