In an isolated container contains 1kg of ice at 0 oC. 1kg of warm water (323K) is poured into the container. How much ice (in kgs) remains after the system returns to thermal equilibrium? (by the end of the process?)

As this is an isolated container, we know that the heat transfer with the environment is zero. Since the specific latent heat of ice is a magnitude bigger than the specific heat of water, the container will still have ice in it, thus the temperature at the end of the process will be 0 ^oC. From these two observations we conclude that the energy lost by the cooling water will be the energy that melts some portion of the ice.               Calculation: first we look at the data we have m_w= m_ice=1kg initially T₁=273K=0 ^oC, T₂= 323K, C_L=335kj/kg and C=4,2kj/kg. From the information in the previous paragraph we build our equation C_L*m_melt= m_wC( T₂-T₁) rearranging this equation we get m_melt= m_wC( T₂-T₁)/ C_L. Plugging in the numbers we arrive at m_melt=0,627kg. This however is not our answer since it is the ice melted to get our result, we must subtract this from the initial weight of the ice. After having done that we get our result which is the amount of ice remaining m=0,373 kg.