Lecture 4 -First law of Thermodynamics (KARIMI)

Question 1

What is the first law of thermodynamics?

Answer 1

The rate of increase in the amount of energy stored in a control volume must equal the rate at which energy leaves the control volume, plus the rate at which energy is generated within the CV. Mathematically: change in Estored=Ein - Eout +Egen. Where E is rate of energy.

Question 2

How can energy be carried to or form the CV?

Answer 2

By heat, work and mass flow.

Question 3

For a steady state system without internal energy generation what is the equation?

Answer 3

m(dot)(h + 0.5v^2 + gz)in - m(dot)(h +0.5v^2 + gz)out + q - W(dot) = 0. h= specific enthalpy, 0.5v^2 + gz = specific potential and kinetic energies, q = net heat transfer rate to cv, W = net rate of work done by cv.

Question 4

If there is no work done and the KEs and PEs are negligible, and the fluid is either a perfect gas or a liquid then:? When do these conditions often hold?

Answer 4

q=m(dot)c_p(Tout - Tin). Often holds inside pipes and channel flow.

Question 5

Energy balance equation for low speed flow (u«c(340m/s)) of most fluids in a pipe?

Answer 5

qconv= m(dot)c_p(Tm,o-Tm,i). Where qconv=convective heat transfer, m(dot)=mass flow rate of fluid, c_p=specific heat capacity, Tm,o and Tm,i = outlet and inlet mean temps of fluid.

Question 6

dqconv =?

Answer 6

dqconv=m(dot)c_pdTm=q”_sPdx
=> dTm/dx = q”_sP/m(dot)c_p = (P/m(dot)c_p)(h(Ts-Tm)).
Last bit is from newton’s law of cooling.

Question 7

For constant heat flux?

Answer 7

qconv = q_s(PL) and dTm/dx=q”_sP/m(dot)c_p which is not equal to f(x).

Question 8

Integration from x=0 for constant heat flux?

Answer 8

Tm(x)=Tm,i + (q”_sP/m(dot)c_p)x , qs=constant.

Question 9

Can you draw a graph relating Tm and Ts for constant heat flux?

Answer 9

Yes or no?

Question 10

qconv=? when Ts=const?

Answer 10

qconv=h(bar)AsdeltaTlm. Where deltaTlm = log mean temp difference = (deltaTo - deltaTi)/ln(deltaTo/deltaTi)