# First Law for the Open System (Control Volume Formulation)

Heat Transfer ( Q ) — Net Rate of Work ( W ) = Net Rate of Energy Flow (across the system boundary)

DE„,

 D_E^ Dt
 + —
 F 2 A V gz m i +————- + —
 Gz
 -Z
 I + —
 — +
 M
 2gc g
 2Sc Scy
 -^out

 Qcv-Wc

Special case of the 1st law is for steady-state flow that has constant flow across the boundary and no mass or energy change in CV.

TOC o "1-5" h z For a typical HVAC system two assumptions are valid: d-E dm

1) Steady-state (—— =0, —— =0) flow across the system boundary

Dt dt

2) KE and PE terms usually small Therefore, for the typical HVAC system:

Qcv-wcv =2>-i-2>-i

Out in

Example 3

A house/building is a thermal system and its envelope is the boundary. Let us consider some energy transfer in a single family house.

 Q infiltration 150 Btu/h Q conduction 200 Btu/h

The thermal mass of the house is assumed to be 700 Btu/°F.

(a) Is the system in equilibrium?

Since Qi„ = Qout, the system is in equilibrium. The heat flows are steady state. The temperature will not change.

(b) What will happen if the A/C is shut off?

O