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hoa [83]
3 years ago
12

Consider a 1000-W iron whose base plate is made of 0.5-cm-thick aluminum alloy 2024-T6 (rho = 2770 kg/m3 and cp = 875 J/kg·°C).

The base plate has a surface area of 0.03 m2. Initially, the iron is in thermal equilibrium with the ambient air at 22°C. Assuming 90 percent of the heat generated in the resistance wires is transferred to the plate, determine the minimum time needed for the plate temperature to reach 220°C.
Engineering
1 answer:
Lesechka [4]3 years ago
5 0

Answer: 79.98sec

Explanation:

Power received by plate = 0.9x1000

= 900W

Volume of metal = area x thickness

V = 0.5x10^-2 x 0.03 = 1.5x10^-4m3

Mass of metal = density x volume

= 2770kg/m3 x 1.5x10^-4 = 0.4155kg

Electrical heat energy = power x time = mass x specific heat capacity(Cp) x temperature change

900 x t = 0.4155 x 875 x (220-22)

900t = 71985.375

t = 79.98s

You might be interested in
6.3.3 Marks on an exam in a statistics course are assumed to be normally distributed
bekas [8.4K]

Answer:

- The calculated p-value (0.392452) is higher than the significance level at which the test was performed, hence, the null hypothesis is true and μ = 60

- 95% Confidence interval for the population mean score = (47.4, 84.1)

Explanation:

The sample of 4 students had scores of 52, 63, 64, 84.

First of, we need to compute the sample mean, we do not need the sample standard deviation as the population variance is given as 5

Mean = (Σx)/N

x = each variable

N = number of variables = 4

Mean = (52 + 63 + 64 + 84)/4

Mean = 65.75

Sample Standard deviation = σ

= √[Σ(x - xbar)²/N]

xbar = mean = 65.75

Σ(x - xbar)² = 532.75

σ = √[532.75/4] = 11.54

in hypothesis testing, the first thing is usually to state the null and alternative hypothesis.

From the question, the null hypothesis has already been stated as

H₀: μ = 60

The alternative hypothesis would then be that the population mean score isn't equal to 60

Hₐ: μ ≠ 60

Since the population distribution is normal and the sample standard deviation is to be used, we use the t-test statistic

t = (x - μ₀)/σₓ

x = sample mean = 65.75

μ₀ = Standard to be compared against = 60

σₓ = standard error = (σ/√n) = (11.54/√4) = 5.77

t = (65.75 - 60)/5.77 = 0.9965 = 1.00

checking the tables for the p-value of this t-statistic

Degree of freedom = df = n - 1 = 4 - 1 = 3

Significance level = 0.05 (95% confidence level)

The hypothesis test uses a two-tailed condition because we're testing in two directions.

p-value (for t = 1.00, at 0.05 significance level, df = 3, with a two tailed condition) = 0.392452

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 0.05

p-value = 0.392452

0.392452 > 0.05

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & say that there is enough evidence to conclude that the populatiom mean score is equal to 60.

b) Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Sample Mean = 65.75

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the t-distribution.

To find the critical value from the t-tables, we first find the degree of freedom and the significance level.

Degree of freedom = df = n - 1 = 4 - 1 = 3

Significance level for 95% confidence interval

(100% - 95%)/2 = 2.5% = 0.025

t (0.025, 3) = 3.18 (from the t-tables)

Standard error of the mean = 5.77

95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]

CI = 65.75 ± (3.18 × 5.77)

CI = 65.75 ± 18.3486

95% CI = (47.4014, 84.0986)

95% Confidence interval = (47.4, 84.1)

Hope this Helps!!!

7 0
3 years ago
While there are many ways to solve this problem, one strategy is to calculate the volume of any metal's unit cell given its theo
IgorC [24]

Answer:

V_{c}=1.396x10^{-28}  m^{3} /unit.cell

Explanation:

z = number of atoms

M = Molar mass of zirconium

N = Avogadro’s number

Vc = volume of zirconium unit cell

d = density

z=12x\frac{1}{6}+2x\frac{1}{2}+3=6

z = 6 atoms per unit cell

M = 91.224 g/mol

N = 6.023x10^{23}  atoms/mol

d = 6.51g/cm^{3}

V_{c}=\frac{zxM}{dxN}

V_{c}=\frac{6x(91.224g/mol)}{(6.51g/cm^{3}) x(6.023x10^{23}atoms/mol) }

V_{c}=1.396x10^{-22}  cm^{3} /unit.cell

V_{c}=1.396x10^{-28}  m^{3} /unit.cell

8 0
3 years ago
A 13.7g sample of a compound exerts a pressure of 2.01atm in a 0.750L flask at 399K. What is the molar mass of the compound?a. 3
Katarina [22]

Answer: Option D) 298 g/mol  is the correct answer

Explanation:

Given that;

Mass of sample m = 13.7 g

pressure P = 2.01 atm

Volume V = 0.750 L

Temperature T = 399 K

Now taking a look at the ideal gas equation

PV = nRT

we solve for n

n = PV/RT

now we substitute

n = (2.01 atm x 0.750 L) / (0.0821 L-atm/mol-K x 399 K )

= 1.5075 / 32.7579

= 0.04601 mol

we know that

molar mass of the compound = mass / moles

so

Molar Mass = 13.7 g / 0.04601 mol

= 297.7 g/mol  ≈ 298 g/mol

Therefore Option D) 298 g/mol  is the correct answer

4 0
3 years ago
The diffusion coefficients for species A in metal B are given at two temperatures:
Kruka [31]

Answer:

a) 149 kJ/mol, b) 6.11*10^-11 m^2/s ,c) 2.76*10^-16 m^2/s

Explanation:

Diffusion is governed by Arrhenius equation

D = D_0e^{\frac{-Q_d}{RT} }

I will be using R in the equation instead of k_b as the problem asks for molar activation energy

I will be using

R = 8.314\ J/mol*K

and

°C + 273 = K

here, adjust your precision as neccessary

Since we got 2 difusion coefficients at 2 temperatures alredy, we can simply turn these into 2 linear equations to solve for a) and b) simply by taking logarithm

So:

ln(6.69*10^{-17})=ln(D_0) -\frac{Q_d}{R*(1030+273)}

and

ln(6.56*10^{-16}) = ln(D_0) -\frac{Q_d}{R*(1290+273)}

You might notice that these equations have the form of  

d=y-ax

You can solve this equation system easily using calculator, and you will eventually get

D_0 =6.11*10^{-11}\ m^2/s\\ Q_d=1.49 *10^3\ J/mol

After you got those 2 parameters, the rest is easy, you can just plug them all   including the given temperature of 1180°C into the Arrhenius equation

6.11*10^{-11}e^{\frac{149\ 000}{8.143*(1180+273)}

And you should get D = 2.76*10^-16 m^/s as an answer for c)

5 0
3 years ago
A 36 ft simply supported beam is loaded with concentrated loads 16 ft inwards from each support. On the left side, the dead load
lana66690 [7]

Answer:

1st part: Section W18X76  is adequate

2nd part: Section W21X62 is adequate

Explanation:

See the attached file for the calculation

8 0
3 years ago
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