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Question
A cylinder containing one gram molecule of the gas was compressed adiabatically until its temperature rose from 27°C to 97°C. Calculate the work done and heat produced in the gas (𝛾 = 1.5).
Solution
Given:
n = 1, 𝛾 = 1.5
Tf - Ti = 97 - 27 = 70°C
We know, R = 8.31 J/mol K
To find:
- Work done (W)
- Heat produced (Q)
Formula: W = `("nR"("T"_"f" - "T"_"i"))/((1 - ϒ))`
Calculation:
From formula,
W = `(1 xx 8.31 xx 70)/(1 - 1.5)`
= -11.63 × 102 J
As work done on the gas is converted into heat, the (rising temperature of the gas,
heat produced, Q = `(11.63 xx 10^2)/4.18` cal ≈ 278 cal
- Work done is -11.63 × 102 J
- The heat produced in the gas 278 cal.
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