Equation for calculating amount of heat transfer through a system boundary.

The equation for calculating amount of heat transfer through a system boundary
when,
T is temperature, an intensive property
X is an extensive property which is result of heat transfer is

a. Q_1-2 = ₁∫² T dX
b. Q_1-2 = ₁∫² X dT
c. Q_1-2 = ₁∫² (1/T) dX
d. none of the above

Correct Answer : a. Q_1-2 = ₁∫² T dX

Explanation :

Heat transfer is also a path function like work transfer. The work involved in a thermodynamic process is give by the equation,

W_1-2 = ₁∫² P dV

where,
p is the pressure and V is the volume of the system.
Whenever there is change in pressure, there will be displacement work. Therefore, pressure difference is a cause and the work transfer is the effect and the change in volume is a result. The quantity of the heat transfer can also be determined as work transfer. In heat transfer process, whenever there is temperature difference, heat transfer takes place and a change is certain extensive property takes place. Thus, temperature is the cause and heat transfer is the effect. Therefore, the heat flow can be determined by

Q_1-2 = ₁∫² T dX.