ENGINEERING COLLEGE

A certain solar energy collector produces a maximum temperature of 100°C. The energy is used in a cyclic heat engine that operates in a 10°C environment. What is the maximum thermal efficiency? What is it if the collector is redesigned to focus the incoming light to produce a maximum temperature of 300°C?

Answers

Answer 1

Answer:

Answer:

$\eta _(max) = 0.2413 = 24.13%$

$\eta' _(max) = 0.5061 = 50.61%$

Given:

$T_(1max) = 100^(\circ) = 273 + 100 = 373 K$

operating temperature of heat engine, $T_(2) = 10^(\circ) = 273 + 10 = 283 K$

$T_(3max) = 300^(\circ) = 273 + 300 = 573 K$

Solution:

For a reversible cycle, maximum efficiency, $\eta _(max)$ is given by:

$\eta _(max) = 1 - (T_(2))/(T_(1max))$

$\eta _(max) = 1 - (283)/(373) = 0.24$

$\eta _(max) = 0.2413 = 24.13%$

Now, on re designing collector, maximum temperature, $T_(3max)$ changes to $300^(\circ)$ , so, the new maximum efficiency, $\eta' _(max)$ is given by:

$\eta' _(max) = 1 - (T_(2))/(T_(3max))$

$\eta _(max) = 1 - (283)/(573) = 0.5061$

$\eta _(max) = 0.5061 = 50.61%$

The answer is "45.3 NM".

There at end of the movement, the forging force is given by

$\to F = Y * \pi * r^2 * [1 + ((2 \mu r)/(3h))]$

h is the final height.

$\to h = (100)/(2)= 50 \ mm$

The ultimate radius is determined by following a volume constancy law, which states that volumes before deformation measured amount following distortion.

$\to \pi * 75^2 * 2 * 100 = \pi * r^2 * 2 * 50\n\n\to 75^2 * 2 = r^2\n\n\to r^2 = 11250\n\n\to r = √(11250)\n\n\to r = 106 \ mm\n\n\to E = \In((100)/(50))\n\n\to E = 0.69\n\n$

You may deduce from the graph flow that $Y = 1000\ MPa$ , thus we use the formula.

$= 1000 * 3.14 * 0.106^2 * [1 + (( 2 * 0.2 * 0.106)/(3 * 0.05))]\n\n= 1000 * 3.14 * 0.011236 * [1 + (( 0.0424)/(0.15))]\n\n= 35.3 * 1.2826\n\n = 45.3 \ MN\n\n\n$

Therefore, the answer is "45.3 NM".

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Answer:

45.3 MN

Explanation:

The forging force at the end of the stroke is given by

F = Y.π.r².[1 + (2μr/3h)]

The final height, h is given as h = 100/2

h = 50 mm

Next, we find the final radius by applying the volume constancy law

volumes before deformation = volumes after deformation

π * 75² * 2 * 100 = π * r² * 2 * 50

75² * 2 = r²

r² = 11250

r = √11250

r = 106 mm

E = In(100/50)

E = 0.69

From the graph flow, we find that Y = 1000 MPa, and thus, we apply the formula

F = Y.π.r².[1 + (2μr/3h)]

F = 1000 * 3.142 * 0.106² * [1 + (2 * 0.2 * 0.106/ 3 * 0.05)]

F = 35.3 * [1 + 0.2826]

F = 35.3 * 1.2826

F = 45.3 MN

Analyze that, “Convection is equal to the Conduction plus fluid flow.”

Answers

Answer:

Conduction is a heat transfer mechanism. It is the dominant heat transfer mechanism in solids and it involves the vibration of the molecules of the solid. As heat is transfered to one end of the solid, the molecules at that end start to vibrate and in this process, collides with the adjacent molecules setting it to vibrate too. Also free electrons around the solid atoms (especially in metals) contribute to this heat flow. The continuous vibration is transfered from molecule to molecule gradually along the solid until the average kinetic energy (a measure of temperature) of the molecules along the metal has increased.

Convection is the dominant heat transfer mechanism in fluids, it involves the complete movement of the fluid molecule from a hot spot in the fluid to a cooler spot in the fluid. For convectional movement to occur, the molecules must first come in contact with the heat and absorb the heat first by conduction. As the heat increases, the fluid molecules break from just vibrating about a fixed point to moving completely to a cooler spot due to buoyant forces (due to the difference in density of hot and cooler fluid molecules). This clearly point out the fact that convectional heat transfer is first conduction, and then complete later flow of the fluid molecules.

A household refrigerator that has a power input of 450 W and a COP of 1.5 is to cool 5 large watermelons, 10 kg each, to 8 C. If the watermelons are initially at 28 C, determine how long it will take for the refrigerator to cool them.

Answers

Answer:

$\Delta t = 5866.667\,s\,(97.778\,m)$

Explanation:

The specific heat for watermelon above freezing point is $3.96\,(kJ)/(kg\cdot K)$ . The heat liberated by the watermelon to cool down to 8°C is:

$Q_(cooling) = (5)\cdot (10\,kg)\cdot (3.96\,(kJ)/(kg\cdot K) )\cdot (20\,K)$

$Q_(cooling) = 3960\,kJ$

The heat absorbed by the household refrigerator is:

$\dot Q_(L) = COP\cdot \dot W_(e)$

$\dot Q_(L) = 1.5\cdot (0.45\,kW)$

$\dot Q_(L) = 0.675\,kW$

Time needed to cool the watermelons is:

$\Delta t = (Q_(cooling))/(\dot Q_(L))$

$\Delta t = (3960\,kJ)/(0.675\,kW)$

$\Delta t = 5866.667\,s\,(97.778\,m)$

Indicate whether the following statements are true or false for an isothermal process: (A) Q=T(∆S). (B) ∆U=0.(C) The entropy change of the system is always zero. (D) The total entropy change of the system and the surroundings is always zero. (E) The entropy change of the surroundings is negative. (F) Q=W.

Answers

Answer:

A=False

B=False

C=False

D=False

E=False

F=False

Explanation:

A. In an isothermal process, only the reversibly heat transfer is 0, $Q_(rev)=T (\Delta S)$

B. Consider the phase change of boiling water. Here, the temperature remains constant but the internal energy of the system increases.

C. This is not true even in reversible process, as can be inferred from the equation in part A.

D. This is only true in reversible processes, but not in all isothermal processes.

E. Consider the phase change of freezing water. Here, the surroundings are increasing their entropy, as they are taking in heat from the system.

F. This is not true if $(\Delta U)\neq 0$ , like in answer B. One case where this is true is in the reversible isothermal expansion (or compression) of an ideal gas.

Calculate the angle of banking on a bend of 100m radius so that vehicles can travel round the bend at 50km/hr without side thrust on the tyres.

Answers

Answer:

11.125°

Explanation:

Given:

Radius of bend, R = 100 m

Speed around the bend = 50 Km/hr = $(5)/(18)*50$ = 13.89 m/s

Now,

We have the relation

$\tan\theta=(v^2)/(gR)$

where,

θ = angle of banking

g is the acceleration due to gravity

on substituting the respective values, we get

$\tan\theta=(13.89^2)/(9.81*100)$

$\tan\theta=0.1966$

θ = 11.125°

The larger the Bi number, the more accurate the lumped system analysis. a)-True b)- False

Answers

Answer:

b). False

Explanation:

Lumped body analysis :

Lumped body analysis states that some bodies during heat transfer process remains uniform at all times. The temperature of these bodies is a function of temperature only. Therefor the heat transfer analysis based on such idea is called lumped body analysis.

Biot number is a dimensionless number which governs the heat transfer rate for a lumped body. Biot number is defined as the ratio of the convection transfer at the surface of the body to the conduction inside the body. the temperature difference will be uniform only when the Biot number is nearly equal to zero.

The lumped body analysis assumes that there exists a uniform temperature distribution within the body. This means that the conduction heat resistance should be zero. Thus the lumped body analysis is exact when biot number is zero.

In general it is assume that for a lumped body analysis, Biot number $\leq$ 0.1

Therefore, the smaller the Biot number, the more exact is the lumped system analysis.

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The answer is "45.3 NM".

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