Here we use the ideal gas law. The volume of the bulb is a constant 200 cm^3. Initially the pressure is 1.1*10^5 pa when the temperature is 25 deg C.
When the bulb is switched on, there is a change in the temperature of the gas. The pressure also changes to 1.8*10^5 pa.
Now the ideal gas law gives P*V= n*R*T
Here V, R and n are constants.
The pressure is proportional to the temperature.
P1 = K*T1
=> 1.1*10^5 = K*(25 + 273)
P2 = K*T2
=> 1.8*10^5 = K*T2
T2 + 273 / 298 = 1.8*10^5 / 1.1*10^5
=> T2 + 273 = 487.63
=> T2 = 214.63
Therefore the new temperature in the bulb is 214.63 degree C.