# 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.