A closed cycle gas turbine unit operating with max. And min. Temp. Of 760 and 20 Celsius deg has a pressure ratio of 7/1. Calculate the thermal efficiency and work ratio?
Ans = 42.7 % , 0.505
My answers are :
Efficiency 42.7 % which is correct.. but work ratio = 1.977.
T1 and T3 are given.T2 is 510.87 and T4 is 592.38.. these values i get it by solving..
Acc. To graph T4 should be less than T2....
Can you solve it for me.. plz
Sure! Let's go through the calculation step by step to find the correct values for the thermal efficiency and work ratio.
First, let's clarify the terminology used in your question:
- T1 = maximum temperature = 760 degrees Celsius
- T3 = minimum temperature = 20 degrees Celsius
- T2 = temperature after compression/expansion = ? (To be calculated)
- T4 = temperature after heat addition/rejection = ? (To be calculated)
- Pressure ratio = 7/1
To find T2 and T4, we can use the equation for the temperature-entropy (T-s) diagram of a closed cycle gas turbine:
(T2 / T1)^((k-1)/k) = (P2 / P1)((k-1)/k) = (P2 / P1)(γ-1)
Where k is the specific heat ratio and γ is the ratio of specific heats.
Given that the pressure ratio is 7/1, we know that P2/P1 = 7.
Now, using the given values of T1 = 760 degrees Celsius and T3 = 20 degrees Celsius, we can find T2 and T4 using the above equation.
First, we need to convert the temperatures from Celsius to Kelvin:
T1 = 760 + 273.15 = 1033.15K
T3 = 20 + 273.15 = 293.15K
Using the equation, we can calculate T2:
(T2 / 1033.15)^((k-1)/k) = 7
To solve this equation, we need to know the specific heat ratio (k) or the ratio of specific heats (γ). Without this information, we cannot calculate T2 accurately or find T4.
Please provide the value of k or γ so that we can proceed with the calculation and find the correct values for T2 and T4.