A Carnot engine takes an amount of heat QH = 113 J from a high-temperature reservoir at temperature TH = 1170°C, and exhausts the remaining heat into a low-temperature reservoir at TL = 13.3°C. Find the amount of work that is obtained from this process
First, convert temperatures to absolute units.
TH = 1443 K
TL = 286.5 K
Carnot Efficiency =
Wout/Qin = (Qin - Qout)/Qin
= 1 - (Tc/Th) = 0.802
Work out = (efficiency)*113 = 90.6 J
hmh
To find the amount of work obtained from the Carnot engine process, we can use the formula for the efficiency of a Carnot engine:
Efficiency = 1 - (TL/TH)
Given the temperatures of the high-temperature reservoir (TH = 1170°C) and the low-temperature reservoir (TL = 13.3°C), we can calculate the efficiency. Let's convert these temperatures to Kelvin since the temperature scale in thermodynamics is in Kelvin.
TH (in Kelvin) = 1170°C + 273.15 = 1443.15 K
TL (in Kelvin) = 13.3°C + 273.15 = 286.45 K
Efficiency = 1 - (286.45 K / 1443.15 K)
Now, we can calculate the efficiency:
Efficiency = 1 - 0.1983
Efficiency = 0.8017
The efficiency of the Carnot engine is 0.8017 or 80.17%.
To find the amount of work obtained from the process, we need to know the amount of heat taken from the high-temperature reservoir (QH = 113 J). The relation between the amount of heat and the amount of work in a Carnot engine is:
Efficiency = Work / QH
Rearranging the formula to solve for work:
Work = Efficiency * QH
Substituting the values:
Work = 0.8017 * 113 J
Calculating the work:
Work ≈ 90.60 J
Therefore, the amount of work obtained from this Carnot engine process is approximately 90.60 Joules.