work vs heat

[Simrina Desar Dis 1H]

There are two equations : Delta U = work(w) and Delta U = heat(q)
Does this mean both work and heat equal each other as well?

[lindsay lathrop 2C]

Those two equations are separate in the sense that Delta U = q is saying "change in internal energy equals heat when heat is transferred and everything else stays the same" and then Delta U = w is saying "change in internal energy equals work when work done is the only thing changing." The case of the latter could come when there is closed system that takes place in a thermally insulated environment.

[Seth_Evasco1L]

I believe that both of those equations are in absence of heat and work respectively.
Delta U = q + w

Delta U = q when there is no work done on or by the system and there is only heat transfer.
Delta U = w when there is no heat transfer and the system has work done on or by it (ex: constant volume in the system).

[Sirajbir Sodhi 2K]

Work and heat are not the same. Work is done when motion is created against an opposing force, while heat is the transfer of energy due to a temperature difference. Work requires an agent -- someone or something must do work. Heat does not require one. Furthermore, when work is done, energy is transferred through the orderly collisions of particles, while for heat, particles collide randomly as they transfer thermal energy through their random motion.

And as the above posters stated, your original equations aren't complete (they leave out the circumstances for when those equations are true).

[Alejandra Rios 1L]

Although these two equations are both correct under specific conditions, these equations are derived from deltaU= q+w. deltaU=q is the equation we can use when no work is being done and has a value of 0, meanwhile deltaU=w is the equation when heat is zero, or not present. That being said, the work and heat are not the same thing.