Which expression is meaningful to describe heat loss of a sy

Which expression is meaningful to describe heat loss of a system at temperature T, internal energy u to

the environment at T0, u0? Assume positive coefficient alpha?

1)Q = alpha(u-u0)

2) Q = alpha(h-h0)

3)Q=alpha(u0-u)

4)Q = alpha(h0-h)

5)Q=alpha(T-T0)

6)Q=alphaT(s-s0)

7)Q=alpha(T0-T)

8)Q=alphaT0(S0-s)

Solution

Using availability function of a closed system ,

Availability = U - T0 S for any system

As the heat is lost its availability reduces and finally the heat transfer can be given by change in availability function .

So, option 8) Q = alpha T0 ( S0 - S) gives the correct energy losss.