A gas is confined to a cylinder fitted with a piston and an electrical heater, as shown here:

Suppose that current is supplied to the heater so that 100 J of energy is added. Consider two different situations. In case (1) the piston is allowed to move as the energy is added. In case (2) the piston is fixed so that it cannot move. (a) In which case does the gas have the higher temperature after addition of the electrical energy?

Video transcript

hi everyone for this problem. It reads shown below is a gas contained in a cylinder with a piston and we see our piston here suppose that 100 and 50 jewels of energy is added to the system. Under these two scenarios, scenario A the piston is allowed to move and scenario B the piston is not allowed to move in which scenario does the gas have higher temperature after the input of energy. And so we want to know after we input 150 jewels of energy, which scenario will the gas have a higher temperature? So for scenario A the piston is not allowed to move. So if this piston excuse me, the piston is allowed to move. So if the piston is allowed to move, what that means is some of the energy input. It is going to be used to move the piston while the rest will be used to heat the gas. So we can say a portion used to heat gas. Okay, so we can write portion of energy. Okay, portion of energy used to heat gas because the other portion is being used to move the piston. However, for scenario B the piston is not allowed to move. So if the piston is not allowed to move then all of the energy inputted will heat the gas since it can't move so well. Right. All of energy used to heat gas. So the question asked, which scenario does the gas have higher temperature. So if all of our energy is being used to heat the gas, this leads to a higher temperature, which makes scenario B the correct answer for this problem. Okay, that's it for this problem. I hope this was helpful.