Consider two glasses, one filled with water and the other half-full, with the water in the two glasses being at the same temperature. In which glass are the water molecules moving faster? In which is there greater internal energy? In which will more heat be required to increase the temperature by 1°C?
Solution 11E Step 1 Provided that, water in both glasses having the same temperature. The average kinetic energy of molecules in a system, K avg (3/2)k B Where, k BBoltzmann constant T - Temperature of the system If the temperatures are same, then the average kinetic energy of water molecules in both glasses will be same in this case. We know that, Average kinetic energy, K avg= (½) mv 2 According to the equation, the speed of water molecules in both glasses will be same. Step 2 The internal energy or thermal energy of a system, E = (3/2Thk T B Where, N - Number of molecules/atoms kB- Boltzmann constant T - Temperature of the system The fulfilled glass contains more number of water molecules and the internal energy of fulfilled glass will be more than the internal energy of half-filled glass.