A 0.2 kg glass cup at 20 C is filled with 0.4 kg of hot water at 70 C. Neglecting any heat losses to the environment, what is the equilibrium temperature?

c1 = 700 J/kg•degr,

c2 = 4180 J/kg•degr,
m1 = 0.2 kg,
m2 = 0.4 kg.
Q1 =c1•m1•(T-20),
Q2 = c2•m2•(70-T)
Q1=Q2.
700•0.2•(T-20) = 4180•0.4•(70-T)
Solve for T

To find the equilibrium temperature, we need to apply the principle of energy conservation. This principle states that the total energy before the system reaches equilibrium is equal to the total energy after equilibrium is reached.

The energy of an object can be calculated using the formula:

Energy = mass x specific heat capacity x change in temperature

For the glass cup, the energy change can be calculated as:

Energy_glass = mass_glass x specific heat capacity_glass x (equilibrium temperature - initial temperature)

Similarly, for the hot water:

Energy_water = mass_water x specific heat capacity_water x (equilibrium temperature - initial temperature)

Since energy is conserved, we can set the total initial energy equal to the total final energy:

Energy_glass + Energy_water = 0

Substituting the values we have:

mass_glass x specific heat capacity_glass x (equilibrium temperature - initial temperature_glass)
+ mass_water x specific heat capacity_water x (equilibrium temperature - initial temperature_water) = 0

Now we can solve this equation. Plugging in the given values:

0.2 kg x specific heat capacity_glass x (equilibrium temperature - 20 C)
+ 0.4 kg x specific heat capacity_water x (equilibrium temperature - 70 C) = 0

Simplifying this equation will give us the equilibrium temperature.

Note: The specific heat capacity for glass is around 840 J/kg·°C, and for water, it is approximately 4200 J/kg·°C.