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2. Heat equations. Prove the following equations for T dS, where we are assuming that the...
6. Prove the following thermodynamic relations using the chain rules and thermodynamic laws. әСр ӘСр Эн...
6. Prove the following thermodynamic relations using the chain rules and thermodynamic laws. әСр ӘСр Эн - Cp -) Сp(1— = (а) әт (b) KT т Р аСр a2v кСу - T эт? ЭР т (c) (d) ЭР V Та - 1 VaT ән V т (ө) (ӘР (g) aP (fav Ср k т н Ср dT эу dP (h) Р 5. Consider a gas of 1 mole that obeys the following equation of state RT P = - a/RTV...
Heat is transferred to a gas in a piston cylinder device so that the volume changes...
Heat is transferred to a gas in a piston cylinder device so that the volume changes from 3 mºto 6 m2. The initial pressure and temperature of the gas are 400 kPa and 25°C. If the process is irreversible determine the following: 1- The final temperature of the gas. 2- The work done during the process (kJ). 3- The total change in internal energy (kJ). 4- The heat transfer for the process (kJ). 5- The total entropy change (kJ/K). Comment...
7. Design an Op Amp circuit that solves the following first order differential equation for v(t):...
7. Design an Op Amp circuit that solves the following first order differential equation for v(t): dv dt 8. Design an Op Amp circuit that solves the following second order differential equations for y(t): 습+10 y(t) = cos(21t) · dt?
(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-...
(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-ay (0)-0, and ax (0)-λ. Here n, μ, and λ are all positive real numbers. This problem involves Laplace transforms, has three parts, and is continued on the next page. You must use Laplace transforms where instructed to receive credit for your solution (a). Define the Laplace Transforms X(s) -|e"x(t)dt and Y(s) -e-"y(t)dt Laplace Transform the differential equations for x(t) and y(t) above, and incorporate...
If p is the price in dollars of computer mice at time, t, then we can think of price as a function of time. Similarly,...
If p is the price in dollars of computer mice at time, t, then we can think of price as a function of time. Similarly, 1. then number of computer mice demanded by consumers at any time, and the number of computer mice supplied by producers at any time, may also be considered as functions of time as well as functions of price. Both the quantity demanded and the quantity supplied depend not only on the price, but also on...
Differentiel equations We consider here, the two masses m1 and m2 connected this time by springs...
Differentiel equations
We consider here, the two masses m1 and m2 connected this time
by springs of stiffnesses k1, k2 and k3 as indicated in the figure
below. We denote by x1 (t) and x2 (t) the movement of each of the 2
masses relative to its static equilibrium position.
1. Prove that the differential equation whose unknown is the
displacement x1 (t) is written in the following form:
2. Deduce the second differential equation whose unknown is the
displacement...
(2) a) An RLC circuit has the following differential equation (DE) for t > 0. d’v(t)/dt...
(2) a) An RLC circuit has the following differential equation (DE) for t > 0. d’v(t)/dt + 10 dv(t)/dt + 16 v(t) = 0) Determine the value of the damping ratio 5, the type of damping, and the form of the natural response for t > 0. Include all values where possible. (7 pts.) b) An RLC circuit has the following differential equation (DE) for t> 0. d’i(t)/dt? +4 di(t)/dt + 9 i(t) = 0 Determine the value of the...
Differential Equations -13 points BoyceDiffEQ10 1.2.007. Ask Your T My Notes A given field mouse population...
Differential Equations
-13 points BoyceDiffEQ10 1.2.007. Ask Your T My Notes A given field mouse population satisfies the differential equation dp 0.2p-310 dt where p is the number of mice and t is the time in months. (a) Find the time at which the population becomes extinct if p(o) 1520. (Round your answer to two decimal places.) month(s) 25.12 (b) Find the time of extinction if p(o) - po, where o< po< 1550. 25.22 month(s) (c) Find the initial population...
A) HIV functions by infecting healthy CD4+T cells, a type of white blood cell, that are...
A) HIV functions by infecting healthy CD4+T cells, a type of white blood cell, that are necessary to fight infection. As the virus embeds in a T cell and the immune system produces more of these cells to fight the infection, the virus propagates in an opportunistic manner. Normally, T cells are produced at a rate s and die at a rate d. The virus, when present in the bloodstream as free virus, infect health T cells at a rate...
4. (25 pts) The Gibb's free energy of a system of N particles is given by,...
4. (25 pts) The Gibb's free energy of a system of N particles is given by, G(T,p)=-Nk T In“- (a) dG = ? (write in differential form similar to dU = TDS - pdV) (b) Find expressions for S and V written as partial derivatives with respect to G. (c) Compute the constant pressure heat capacity Cp of the system: C=T(dS/dT), Hint: Use your expression for S derived in (b) above, 3333333 (d) Extract the equation of state for this...
6. Prove the following thermodynamic relations using the chain rules and thermodynamic laws. әСр ӘСр Эн - Cp -) Сp(1— = (а) әт (b) KT т Р аСр a2v кСу - T эт? ЭР т (c) (d) ЭР V Та - 1 VaT ән V т (ө) (ӘР (g) aP (fav Ср k т н Ср dT эу dP (h) Р 5. Consider a gas of 1 mole that obeys the following equation of state RT P = - a/RTV...
Heat is transferred to a gas in a piston cylinder device so that the volume changes from 3 mºto 6 m2. The initial pressure and temperature of the gas are 400 kPa and 25°C. If the process is irreversible determine the following: 1- The final temperature of the gas. 2- The work done during the process (kJ). 3- The total change in internal energy (kJ). 4- The heat transfer for the process (kJ). 5- The total entropy change (kJ/K). Comment...
7. Design an Op Amp circuit that solves the following first order differential equation for v(t): dv dt 8. Design an Op Amp circuit that solves the following second order differential equations for y(t): 습+10 y(t) = cos(21t) · dt?
(6). The quantities x(t) and y(t) satisfy the simultaneous equations dt dt dx dt where x(0)-y(0)-ay (0)-0, and ax (0)-λ. Here n, μ, and λ are all positive real numbers. This problem involves Laplace transforms, has three parts, and is continued on the next page. You must use Laplace transforms where instructed to receive credit for your solution (a). Define the Laplace Transforms X(s) -|e"x(t)dt and Y(s) -e-"y(t)dt Laplace Transform the differential equations for x(t) and y(t) above, and incorporate...
If p is the price in dollars of computer mice at time, t, then we can think of price as a function of time. Similarly, 1. then number of computer mice demanded by consumers at any time, and the number of computer mice supplied by producers at any time, may also be considered as functions of time as well as functions of price. Both the quantity demanded and the quantity supplied depend not only on the price, but also on...
Differentiel equations
We consider here, the two masses m1 and m2 connected this time
by springs of stiffnesses k1, k2 and k3 as indicated in the figure
below. We denote by x1 (t) and x2 (t) the movement of each of the 2
masses relative to its static equilibrium position.
1. Prove that the differential equation whose unknown is the
displacement x1 (t) is written in the following form:
2. Deduce the second differential equation whose unknown is the
displacement...
(2) a) An RLC circuit has the following differential equation (DE) for t > 0. d’v(t)/dt + 10 dv(t)/dt + 16 v(t) = 0) Determine the value of the damping ratio 5, the type of damping, and the form of the natural response for t > 0. Include all values where possible. (7 pts.) b) An RLC circuit has the following differential equation (DE) for t> 0. d’i(t)/dt? +4 di(t)/dt + 9 i(t) = 0 Determine the value of the...
Differential Equations
-13 points BoyceDiffEQ10 1.2.007. Ask Your T My Notes A given field mouse population satisfies the differential equation dp 0.2p-310 dt where p is the number of mice and t is the time in months. (a) Find the time at which the population becomes extinct if p(o) 1520. (Round your answer to two decimal places.) month(s) 25.12 (b) Find the time of extinction if p(o) - po, where o< po< 1550. 25.22 month(s) (c) Find the initial population...
A) HIV functions by infecting healthy CD4+T cells, a type of white blood cell, that are necessary to fight infection. As the virus embeds in a T cell and the immune system produces more of these cells to fight the infection, the virus propagates in an opportunistic manner. Normally, T cells are produced at a rate s and die at a rate d. The virus, when present in the bloodstream as free virus, infect health T cells at a rate...
4. (25 pts) The Gibb's free energy of a system of N particles is given by, G(T,p)=-Nk T In“- (a) dG = ? (write in differential form similar to dU = TDS - pdV) (b) Find expressions for S and V written as partial derivatives with respect to G. (c) Compute the constant pressure heat capacity Cp of the system: C=T(dS/dT), Hint: Use your expression for S derived in (b) above, 3333333 (d) Extract the equation of state for this...
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