We have a 4 yr. old gas hot water heater. A few months ago (hot summer) we noticed our therm use was 3x's more for the summer months than last summer. Our plumber determined our t & p valve was not working and he has replaced it. Could you please tell me why a faulty t & p valve caused us to use so many gas therms?

t = temperature, p = pressure. When the limits are exceeded the valve literally dumps water down the drain. It's typically located at the top of the heater with a piece of pipe on it. If it's in the basement, sometimes it drains into the french drain. If it's faulty, it dumps when it's not supposed to, thus wasting water and gas.

You hot water tank had an effective leak. You water bill will go up too.

It would seem to me that it would take a large discharge through the T&P valve to increase usage that much. Is it piped to a drain or outside where you wouldn't see it leaking? It should be on the side near the top. Do you have city water? If so, they may have installed a back flow preventer. Without an expansion tank, that will cause the T&P to open. Once it opens, it often get crud in it and leaks until cleaned or replaced. I would keep a close eye on things at least the next month or 2.