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What is the final temperature of 0.10 mole monatomic ideal gas that performs 75 cal of work adiabatically if the initial temperature is 227 $^{o}C$ ?
A. 250 K
B. 300 K
C. 350 K
D. 750 K

seo-qna
Last updated date: 13th Jun 2024
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Answer
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Hint: For an adiabatic process the work done is as follows.
W = nCdT
W = work done
N = number of moles
dT = Difference in temperatures (initial and final temperatures)
C = $\dfrac{3}{2}R$
R = gas constant

Complete Solution :
- In the question it is asked to calculate the temperature of monatomic ideal gas which is under adiabatic condition.
- We have to calculate the final temperature and have to find which option is correct among the given options.
- In the question it is given that the initial temperature is 227$^{o}C$ = 227 + 273 = 500 K.

- For an adiabatic process the work done is as follows.
W = nCdT
 W = work done = 75 cal
N = number of moles = 0.10 moles
dT = Difference in temperatures (initial and final temperatures) = (T-500K)
C = $\dfrac{3}{2}R$
R = gas constant = 2cal/K mol

- Substitute all the known values in the above formula to get the Temperature T.
\[\begin{align}
 & 75=\dfrac{3}{2}\times 0.10\times 2\times (T-500) \\
 & T-500=\dfrac{75}{0.3} \\
 & T=500+250=750K \\
\end{align}\]
- Therefore the final temperature of monatomic ideal gas which is under adiabatic condition is 750 K.
So, the correct answer is “Option D”.

Note: Adiabatic process means it is a type of thermodynamic process that occurs without the change in mass of the system and its surroundings. But in adiabatic processes energy is going to transfer in the forms of work done.