A gas with initial state variables p₁, V₁, and T₁ expands isothermally until V₂=2V₁. What are (a) T₂

Video transcript

Hello, fellow physicists today, let's solve the following practice problem together. So first off, let's read the problem and highlight key pieces of information to see what exactly we're solving for. So P zero V zero and T zero describe the beginning state variables for a gas sample that experiences a isothermal expansion to a point V one equals four V zero. Find T one the temperature at V one. OK. So we're given some multiple choice answers. So A is 1.4 T zero, B is 0.25 T zero and C is T zero unchanged and D is four T zero. OK. So right off the bat, we should be able to recall that when we're dealing with an iso thermal conditions that it will mean that it's equal to a temperature that is constant. OK. So isothermal conditions means that the temperature is constant. OK. So with that in mind, since the gas is expanding isothermal, the gas itself will expand at a constant temperature. So the temperature, so T equals constant. So if temperature T is constant, we can go ahead and write the following mathematical statement that T one equals T zero. Where T one is, the final temperature is equal to T zero. The initial temperature. Thus, we can write without a doubt that T zero, that T zero will be unchanged. T zero is unchanged because the initial temperature and the final temperature are equal to each other. OK. So that would mean that our final answer is C T zero. Unchanged. Thank you so much for watching. I can't wait to see you in the next video. Bye.