If the battery was removed, the energy produced by the battery would not be able to continue its path along the circuit.
There is a specific formula to use for these type of problems.
ln (P2/ P1)= Δvap/ R x (1/T1 - 1/T2)
R= 8.314
P1= 92.0 torr
T1= 23 C + 273= 296 K
P2= 351.0 torr
T2= 45.0 C + 273= 318 K
plug the values and solve for the unknown
ln( 351.0/ 92.0)= Δvap/ 8.314 x (1/296 - 1/318)
Δvap= 47630.6 joules
The main purpose of scientific methods, is to show the variations of the topic you are doing in science and how you are proving it to be that way.