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Sindrei [870]
3 years ago
15

1. How much heat is absorbed by a 50g iron skillet when its temperature rises from 10oC to 124oC? Joules

Mathematics
1 answer:
hoa [83]3 years ago
7 0
<span>1. How much heat is absorbed by a 50g iron skillet when its temperature rises from 10oC to 124oC? Joules

Formula: Heat = mass * specific heat * ΔT

Data:
mass = 50 g = 0.050 kg
specific heat of iron = 450 J/ kg °C
ΔT = 124°C - 10°C ¿ 114 °C

=> heat = 0.050kg * 450 J / kg°C * 114°C ≈ 2.6 J

2. If a refrigerator is a heat pump that follows the first law of thermodynamics, how much heat was removed from food inside of the refrigerator if it released 492J of energy to the room? Joules

The firs law of thermodynamics is conservation of energy => energy removed from inside of the refrigerator = energy released to the room

=> Answer = 492 J

3. How much heat is needed to raise the temperature of 45g of water by 63oC? Joules

Formula: heat = mass * specific heat * ΔT

specific heat of water = 4186 J / Kg °C

heat = 0.045 kg * 4186 J/kg °C * 63°C = 11,867.31 J
</span>
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NarStor, a computer disk drive manufacturer, claims that the median time until failure for their hard drives is more than 14,400
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Answer:

The test statistics is  t  =  -1.727

Step-by-step explanation:

From the question we are told that

The data given is  

   330 620 1870 2410 4620 6396 7822 81028309 12882 14419 16092 18384 20916 23812 25814

 The population mean is  \mu  =  14400

    The  sample  size is  n =  16

  The  null hypothesis is  \mu \le  14400

    The  alternative hypothesis is  H_a  :  \mu > 14400

The sample mean is mathematically evaluated as

  \= x  =  \frac{\sum x_i}{n}

So

   \= x  =  \frac{330+ 620+ 1870 +2410+ 4620+ 6396+ 7822+ 8102+8309+ 12882+ 14419+ 16092+ 18384 +20916+ 23812+ 25814 }{16}

=>  \= x = 10799.9

The  standard deviation is mathematically represented as

      \sigma =\sqrt{\frac{ \sum (x_i - \=x)^2}{n}}

So

\sigma =\sqrt{\frac{(330- 10799.9)^2 + (620- 10799.9)^2+ (1870- 10799.9)^2 +(2410- 10799.9)^2 + (4620- 10799.9)^2 +(6396- 10799.9)^2 +(7822- 10799.9)^2 }{16}}  \ ..

   ..\sqrt{ \frac{(8102 - 10799.9)^2 +(8309 - 10799.9)^2 + (12882 - 10799.9)^2 + (14419 - 10799.9)^2 + (16092 - 10799.9)^2 + (18384 - 10799.9)^2 +(20916 - 10799.9)^2  }{16}} \ ...

  \ ... \sqrt{\frac{(23812 - 10799.9)^2 +(25814 - 10799.9)^2 }{16}}

=>  \sigma  =  8340

  Generally the test statistic is mathematically represented as

  t =  \frac{10799.9- 14400}{ \frac{8340}{\sqrt{16} } }

t  =  -1.727

From the z-table  the p-value is  

     p-value  = P(Z > t) =  P(Z >  -1.727) =  0.95792

 From the values obtained we see that

        p-value  >  \alpha  so we fail to reject the null hypothesis

Which implies that the claim of the NarStor is wrong

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