How to determine heat from resistance?

[Thundagere]

Is there a formula of some sorts that can determine the thermal energy released from electricity flowing through a wire, knowing the wire's resistance?

 

[sankalpmittal]

Is there a formula of some sorts that can determine the thermal energy released from electricity flowing through a wire, knowing the wire's resistance?

Yes , there is formula. You can even derive it logically. You can do it! Work done=Energy manifested is a basic logical equation in fundamental physics.

Thermal energy released from wire due to its heating = I²RT
Thermal energy is not released from electricity. It is released due to resistance in a wire because work is done on per unit charge to move it through certain displacement in a wire. On moving a unit charge it faces obstruction or friction of wire. This work done is manifested in form of heat energy in a wire.

You know ,
V=W/Q
W=VQ
So Heat energy released or work done by wire :
Thermal energy released from wire due to its heating = VQ
Thermal energy released from wire due to its heating = IR x IT
Thermal energy released from wire due to its heating = I²RT

Where I is current flowing in wire , R is resistance and T is time.

R=k l/a
a is area of cross section in a wire and l is length of wire.
k is (rho) or resistivity in a wire.

Thermal energy released from wire due to its heating = k I² T l/a