Heat transfer equation (temperature difference)

[MechaMZ]

Homework Statement

For the equation mc$$\Delta$$T, i suppose $$\Delta$$T should be T_f - T_i.

However, at what condition we should let $$\Delta$$T be T_i - T_f?

I did come across a question which requires $$\Delta$$T be T_i - T_f for a heat lost by an object.

eg,
heat lost by copper = heat absorbed by beaker & water
mc(T_i - T_f) = m_beakerc_beaker(T_f - T_i) + m_waterc_water(T_f - T_i)

I think perhaps we need to let mc$$\Delta$$T as a positive value since it just a magnitude? however, the value is not the same(pretty close) if i let it be T_i - T_f.

Need help, thanks =)

 

[MechaMZ]

anyone knows?

 

[Mapes]

$mc\Delta T=mc(T_f-T_i)$ is always the energy gained. The energy lost by the copper was then $-mc\Delta T$, which is equivalent to the other expression.

 

[MechaMZ]

however, for the example above, why the initial temp and final temp is reversed?

 

[Mapes]

Because $-mc(T_f-T_i)=mc(T_i-T_f)$. Is this what you mean?

 

[MechaMZ]

so we should write heat lost by copper as negative since the heat is released out, but the result of $-mc(T_f-T_i)$ will still be positive right?

 

[Mapes]

If you're saying that we should include the minus sign prefactor because we're considering the amount of energy leaving, but that the sign of $-mc(T_f-T_i)$ is positive because $T_f<T_i$, I agree.