Solution Found!
Cooling method for gas turbines. During periods of high
Chapter 7, Problem 40E(choose chapter or problem)
Cooling method for gas turbines. During periods of high electricity demand, especially during the hot summer months, the power output from a gas turbine engine can drop dramatically. One way to counter this drop in power is by cooling the inlet air to the gas turbine. An increasingly popular cooling method uses high-pressure inlet fogging. The performance of a sample of 67 gas turbines augmented with high-pressure inlet fogging was investigated in the Journal of Engineering for Gas Turbines and Power (Jan. 2005). One measure of performance is heat rate (kilojoules per kilowatt per hour). Heat rates for the 67 gas turbines are listed in the table below. Suppose that a standard gas turbine has, on average, a heat rate of 10,000 kJ/kWh. Conduct a test to determine if the mean heat rate of gas turbines augmented with high-pressure inlet fogging exceeds 10,000 kJ/kWh. Use \(\alpha=.05 \text {. }\)
\(\begin{array}{rrrrrrrrrr}
\hline 14622 & 13196 & 11948 & 11289 & 11964 & 10526 & 10387 & 10592 & 10460 & 10086 \\
14628 & 13396 & 11726 & 11252 & 12449 & 11030 & 10787 & 10603 & 10144 & 11674 \\
11510 & 10946 & 10508 & 10604 & 10270 & 10529 & 10360 & 14796 & 12913 & 12270 \\
11842 & 10656 & 11360 & 11136 & 10814 & 13523 & 11289 & 11183 & 10951 & 9722 \\
10481 & 9812 & 9669 & 9643 & 9115 & 9115 & 11588 & 10888 & 9738 & 9295 \\
9421 & 9105 & 10233 & 10186 & 9918 & 9209 & 9532 & 9933 & 9152 & 9295 \\
16243 & 14628 & 12766 & 8714 & 9469 & 11948 & 12414 & & & \\
\hline
\end{array}\)
Questions & Answers
QUESTION:
Cooling method for gas turbines. During periods of high electricity demand, especially during the hot summer months, the power output from a gas turbine engine can drop dramatically. One way to counter this drop in power is by cooling the inlet air to the gas turbine. An increasingly popular cooling method uses high-pressure inlet fogging. The performance of a sample of 67 gas turbines augmented with high-pressure inlet fogging was investigated in the Journal of Engineering for Gas Turbines and Power (Jan. 2005). One measure of performance is heat rate (kilojoules per kilowatt per hour). Heat rates for the 67 gas turbines are listed in the table below. Suppose that a standard gas turbine has, on average, a heat rate of 10,000 kJ/kWh. Conduct a test to determine if the mean heat rate of gas turbines augmented with high-pressure inlet fogging exceeds 10,000 kJ/kWh. Use \(\alpha=.05 \text {. }\)
\(\begin{array}{rrrrrrrrrr}
\hline 14622 & 13196 & 11948 & 11289 & 11964 & 10526 & 10387 & 10592 & 10460 & 10086 \\
14628 & 13396 & 11726 & 11252 & 12449 & 11030 & 10787 & 10603 & 10144 & 11674 \\
11510 & 10946 & 10508 & 10604 & 10270 & 10529 & 10360 & 14796 & 12913 & 12270 \\
11842 & 10656 & 11360 & 11136 & 10814 & 13523 & 11289 & 11183 & 10951 & 9722 \\
10481 & 9812 & 9669 & 9643 & 9115 & 9115 & 11588 & 10888 & 9738 & 9295 \\
9421 & 9105 & 10233 & 10186 & 9918 & 9209 & 9532 & 9933 & 9152 & 9295 \\
16243 & 14628 & 12766 & 8714 & 9469 & 11948 & 12414 & & & \\
\hline
\end{array}\)
Step 1 of 3
Here We have to test the claim that the mean heat rate of gas turbines augmented with high pressure inlet fogging exceeds 10,000kj/kWh
Null hypothesis \(H_0\): the mean heat rate of gas turbines augmented with high pressure inlet fogging is 10,000kj/kWh
Then \(H_{0}: \mu=10,000\)
Alternative hypothesis \(H_1\): the mean heat rate of gas turbines augmented with high pressure inlet fogging exceeds 10,000kj/kWh
Then \(H_{1}: \mu>10,000 \text { (Right tailed test) }\)