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Mobil 1 5W-30 Fully Synthetic with SuperSyn Technology, is the approved oil for the Corvette. The oil must specify that it meets GM 4718M (Corvette spec).
Following is from the 2003 Corvette Owner's Manual, Section 5, Service and Appearance Care (I would think yours should read much the same):
What Kind of Engine Oil to Use
Look for two things:
GM4718M
Your vehicle’s engine requires a special oil meeting GM Standard GM4718M. Oils meeting this standard may be identified as synthetic. However, not all synthetic oils will meet this GM standard. You should look for and use only an oil that meets GM Standard GM4718M.
Notice: If you use oils that don’t have the GM4718M Standard designation, you can cause engine damage not covered by your warranty.
SAE 5W-30
As shown in the viscosity chart, SAE 5W-30 is best for your vehicle. However, you can use SAE 10W-30 if it’s going to be 0°F (-18°C) or above. These numbers on an oil container show its viscosity, or thickness. Do not use other viscosity oils such as SAE 20W-50.
Oils meeting these requirements should also have the starburst symbol on the container. This symbol indicates that the oil has been certified by the American Petroleum Institute (API). You should look for this on the oil container, and use only those oils that are identified as meeting GM Standard 4718M and have the starburst symbol on the front of the oil container. Your vehicle’s engine is filled at the factory with a Mobile 1® synthetic oil. which meets all requirements for your vehicle.
Substitute Engine Oil: When adding oil to maintain engine oil level, oil meeting GM Standard GM4718M may not be available. You can add substitute oil designated SAE 5W-30 with the starburst symbol at all temperatures. If temperatures are above 0°F (-18°C), you may substitute SAE 10W-30 with the starburst symbol. Substitute oil not meeting GM Standard GM4718M should not be used for an oil change.
Engine Oil Additives
Don't add anything to your oil. The recommended oils with the starburst symbol are all you will need for good performance and engine protection.
When it comes to synthetic oil, 10w30 is obsolete, because the 5w30 can do everything the 10w30 can do, but with the added benefit of flowing quicker on startup.
When it comes to synthetic oil, 10w30 is obsolete, because the 5w30 can do everything the 10w30 can do, but with the added benefit of flowing quicker on startup.