Imagine that you have a gas confined in an insulated cylinder by a piston. Imagine that you suddenly push hard on the piston, compressing the gas to one-half its volume. Then you slowly let the gas expand back to its original volume. Will the gas have the same temperature as when you started? Will its entropy be the same as before? Would your answers be different if you had slowly compressed the gas and then slowly expanded it? Explain your responses carefully.