Starting with an expression for U(S.V), show that m(V) = (dU/dV)T is given by Tt(v)= (dp/dT)V-P.
Starting with an expression for U(S,V) , show that π(v) = (dU/dV)T is given by π(v)= (dp/dT)V - p .
TT 3 3 3 Evaluate the integral 4 cos (u + v + w) du dy dw. ws kle 4 cos (u + v + w) du dv du = (Type an exact answer, using and radicals as needed
solve Question 6: Given that v(0) = 2 and dv(0)/dt = 4, solve the following second-order differential equation d- du ( +54 + 60 = 10e-'u(t) dt 4 marks
Solve the differential equation for P(t) Ri dI(t) P(t) dP(t) dt dt Ri dI(t) P(t) dP(t) dt dt
Part A Starting with the van der Waals equation of state, find an expression for the total differential dP in terms of dV and dT Match the expressions in the left column to the appropriate blanks in the equations on the right. Help Reset Dr (V-b) Dv V-b RT dT )dV + dP= V RT V-b 2a VD RT (V-b)3 RT In RT V-b Vnt 2(V-b) RT Vtb RT (V-b)
Given that no-5 and dv(0)/dt-10, solve-it2t) + 6U-30 e-tu (t). + 5 -t 2t V(t) is calculated as | e3 u(t)
let that is U + V not U + U A) complete dw/du and dw/dv B) complete d2w/dadv e w 14 + 1
of the a) (5 p) Interpret the rocket equation dv(t)M(t)=-udM(t) [EQ.1) within the framework law of momentum conservation, written in a closed system; here M(t) is the rocket mass, at time t, whereas dM(t) is by definition, dM(t)=M(t+dt)-M(t); dM(t)=|dM(t), is the mass of the gas thrown by the rocket through the infinitely small period of time dt; on the other hand, dv(t) is, still by definition, dv(t)=v(t+dt)-v(t), i.e. the increase in the velocity of the rocket through the period of...
Assuming U=U(T,V) write an expression for the total change, dU. If dU is an exact differential, how would you know and what would this mean?
a) (5 p) Interpret the rocker equation dv(t)M(t)=-udM(t) (EQ.1) within the framework of the law of momentum conservation, written in a closed system, here M(t) is the rocker mass, at time t, whereas M(t) is by definition, dM(t)-M(t+dt)-M(t): - dM(t)-dM(t), is the mass of the gas thrown by the rocket through the infinitely small period of time dt; on the other hand, dv(t) is, still by definition, dv(t)-v(t+dt)-v(t), i.e. the increase in the velocity of the rocker through the period...