Hot water went out. Installed new 40 gallon electric water heater. Heater seems to be fine, everything checked out with VOM. Water in tank is hot out of PRV, but hot water in entire house is only warm +- 105 deg. When cold water supply is shut off to water heater, and hot water is turned on in sink, get a lot of cold water. Is this normal?
Please help.

You have probably burn your element during your trouble shoting cause if you turn off cold supply to heater and drain it while waterheater is on then you may burn up the element also the rest of your post does not make sense

I am fairly certain you did not burn out your heater element since the problem was there before you started trouble shooting. However, do not shut off the cold supply to the tank and draw hot water again, you'd be tempting fate. Also do not test water temp via the PRV since there is a slight chance it will not always reseal perfectly as the unit ages. Try the drain valve at the bottom of the tank. That water should be around 120 degrees depending on how high you have set your stat. Check your water temp on hot only at a fixture with no screen or aerartoe like the basth tube spout, what is that temp? What is your voltage on this unit and does it have one or two elements? Back to you.