Immersion heaters and kettles are VERY efficient, 90% +. If it makes you feel happier, by all means buy a new one, but " If it ain't broke, don't fix it " is a very good motto. I'd put money on it that a new one will be no more efficient, but won't last nearly as long as the old one.
If you want the heater to be more effective, there are 2 simple things you can do 1. Descale the tank if you are in a hard water area. Scale on the elements acts as a heat insulator so the elements run hotter and take longer to heat the water.
After descaling, be careful, as the water temperature may increase significantly, because scale on the thermostat tube may cause the thermostat to be inaccurate. You may need to tweak it a few times to get the temperature how you want it. 2.
Put thicker insulation around the tank. When a heater element ages, it doesn't become any less efficient, but when it gets thin its resistance increases so it takes less current - effectively its power reduces. You can easily check the heater power by turning off everything else in the home, reading the electric meter and switching both heating elements on.
Time it for, say 15 minutes so you can be sure the water won't have heated fully, i.e. The elements will be on all the time. Take the first meter reading from the second and multiply by four.
That should give you the power of the heaters. The plate says total watts 2500 so your answer should be 2.5 (+/- 10%).
Modern gas or electric water heaters will save you about 25% on energy costs as your 50 year old heater will have little or no insulation and heating controls will be non existent. Ask your plumber to provide you with installation estimates and expected running costs, the most reliable and long lasting will have a 12 year guaranteed life. Different systems range from roof top solar thermal (free energy costs in high summer) air or ground source heat pump, gas water heater with flue gas reclurculation, non storage water heaters.
You will need a basement with sufficent headroom for some of the tall solar storage hot water cylinders. You may want to ask your plumber for an estimate of the costs to install insulated secondary pumped hot water circulation loop pipework to supply all locations serving bathrooms /toilets requiring hot water, so eliminating the water draw off delay to get hot water at outlets.
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