Hello, So I have been struggling to understand internal energy for quite a long time and I hope you will be able to help me get straight with it. The most common definition I find on the internet is "The sum of the kinetic and potential energy of the molecules/atoms in a system" (often gases). Too me, this sounds like a physical quantity bigger than the heat energy, because the latter takes only the kinetic energy of the molecules in account (Am I wrong?). But the equation for internal energy is: ΔU = ΔQ - W = ΔQ - p × ΔV where ΔU is the change in internal energy, ΔQ the heat given to the system and W (or pΔV) the work done by the system (often change in volume). So this means that the change of internal energy is smaller than the change in heat. I would be really thankful if somebody could explain the differences between heat and internal energy, and give the proper definitions of them. What confuses me even more is the following example in my physics book: 1. The problem statement, all variables and given/known data "A closed glass cylinder has a piston which can be assumed to move very easily and without friction. The cylinder contains 1,0 dm^3 of air with a temperature of 20 degrees Celsius and has a pressure equivalent to 101,3 kPa. The air is then heated to 100 degrees Celsius. a) How much heat was given to the air? b) How big is the work done by the system by change in volume? c) What's the change in internal energy?" 2. Relevant equations and information ΔU = ΔQ - W = ΔQ - p × ΔV (1) pV=nRT → V1/T1=V2/T2 (2) ΔE = mcΔT (3) specific heat capacity of air c = 1,01 kJ/(kg × K) ρ = m/V (4) density of air = 1,293 kg/m^3 3. The solution in the book a) The heat energy required to increase the air's temperature by 80 degrees is calculated with equation (3), with the help of equation (4) to determine the mass of the air. This gives the answer: 104 J b) The pressure is assumed to be constant (thanks to the very mobile piston), and so the change in volume can be calculated with equation (2). This value is then multiplied with the magnitude of the pressure (101,3 kPa) and so the work done by the system is determined to be 28 J. c) With the help of equation (1) the change in internal energy is calculated to be: 104-28= 77 J. 3. What I don't understand and need help with I understand the calculations, but once again I can't really link it to the definitions for heat and internal energy. What I find the most incomprehensible is how we can say that 104 J go to increase the temperature of the air, when we know that 28 J of these will go to expand the cylinder! I would find it more logical to say that only 77 J go to heat the gas, but then this would lead to the conclusion that heat is equal to internal energy, which is certainly not right according to equation (1). Big thanks to somebody who can make the definitions of internal energy and heat clear, and explain why we can say that 104 J heat the system when we know that 28 J will go to work!