Yes, an automobile use more gasoline if the radio volume is turned up while driving on the highway
The reason is simple, when the volume is turned up, the speakers will start to consume more electrical energy (from the battery of vehicle) to produce more sound energy,
The battery is charged by the mechanical energy produced by the engine. Hence engine will consume more gasoline to produce enough mechanical energy that can be used to charge the battery and from there to produce sound energy.
Chemical energy (fuel) ---> Mechanical energy (engine) ----> electrical energy (battery) -----> sound energy (speakers)
So when the volume is increased, more sound energy will be required, which will consume for fuel (gasoline)
(Note that the extra fuel consumption will be negligibly small for a range of time)
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