Why is the intake valve of an engine generally larger than the exhaust valve?

The main reason for the size difference is to avoid pre-ignition and knocking. The exhaust valve is the hottest part of the engine. We also know that Q=m Cv dT.
Hence the heat generated is directly proportional to the mass of the substance. Now if the size of the exhaust valve increases, its mass increases. So the heat of the valve increases.

Now after the exhaust stroke, the charge(air and fuel) is sucked in for the next cycle. If the temperature of the exhaust is very high it may cause pre ignition.

Also even if the temperature of the valve is not that high, during compression the charge becomes more volatile. The exhaust valve will ignite the charge creating a flame front which progresses in all directions. Also the spark plug creates a flame front. When these two flame fronts meet, knocking takes place.
To avoid these difficulties the exhaust valve size is kept smaller than the inlet valve.

Both inlet valve and exhaust valve approximately handle the same amount of air, though exhaust valve exhausts slightly more mass due to fuel addition (CI engine). The time for which both these valves are operated is nearly the same, so they need to get the same amount of mass in/out in same amount of time.

Now, when the inlet valve inducts air, the pressure difference between the chamber and ambient is quite small. On the other hand, the exhaust valve has a large pressure difference to assist the exhaust of burnt gases due to larger pressures at the starting of exhaust stroke. In fact, the exhaust valve has to be opened a little early to avoid large pressures (Exhaust blow-down).

Due to these differences in pressure difference during intake and exhaust, it is tougher to induct the air than to exhaust the burnt gases. Hence the intake valve has to be bigger than the exhaust valve.

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