thanks in advance! Find an expression for beta of the liquid in terms of T, h_o,
ID: 1432895 • Letter: T
Question
thanks in advance!
Find an expression for beta of the liquid in terms of T, h_o, deltah, and constants. (deltah may be assumed small enough to be treated as dh) The connecting tube may be considered of negligible volume. Note that you should approach the problem by equating pressures; you should not assume a e original volumes on each side remain constant, since liquid may move from one tube to the other during the expansion. Prove by differential calculus, for small changes of temperature, dT, that: where F is the buoyant force on a body of volume V_o and linear expansion coefficient alpha submerged in a liquid of initial density p_o and volume coefficient of expansion beta. Assuming no heat loss from the system,fmd the rise in temperature of the liquid (and brake), in terms of R, c, and omega. ( Be alert in writing the work-energy equation for the problem. Does the K.E. increase when the blocks come in?) How long could a 2000 hp motor be operated on the heat energy liberated by one cubic mile of ocean water when the temperature is lowered by 1 Cdegree, if all of this heat were converted to mechanical energy? Why do we not utilize this tremendous reservoir of energy? Compute the heat required to raise the temperature of a mass m of the substance from 0 degreeC to TdegreeC. The specific heat capacity c of a substance is given by the empirical equation c = a + bT^2, where a and b are constants and T is the centrigrade temperature. What is the mean specific heat of the substance in the temperature range between 0degreeC and T degreeC? Compare this with the true specific heat at a temperature midway between 0 degreeC and T degreeC. At very low temperatures, in the neighborhood of absolute zero, the specific heat of solids is given by the Debye equation, c = pT^3, where T is the absolute or Kelvin temperature and p is a constant, different for different materials. Compute the heat required to raise the temperature of a mass m of a solid from 0 K to 10 K. Compute the mean specific heat in the temperature range between 0 K and 10 K. Compute the true specific heat at a temperature of 10 K.Explanation / Answer
1975) Heat required to raise a body of mass m by Dt is
dQ=mcdT
Heat requird to raise from 0 to T is
dQ=mc integral 0 to T dT
(c=a+bT2)
dQ=integral 0 to T (m*(a+bT2) dT
dQ=m integral 0 to T(bT2)dT
dQ=mb T3/3
b)Mean specific heat capacity ,Cp/R=A+BT+CT2+D/T2
Where A , B, C, and D are constants
c) Let us consider the midway temperature is some arbitory value, let it be 10 o C
S0, Cp/R=A+10B+100C+0.01D
1871 is not there in the question paper
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