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In a thermodynamic process, the pressure of a fixed mass of a gas is changed in such a manner that the gas releases $20 J$ of heat and $8 J$ of work is done on the gas. If the initial internal energy of the gas was $30 J$ , then the final internal energy is $9 x$ . Find the value of $' x'$ .

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answer is 2.

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Detailed Solution

$d Q = - 20 J, d W = - 8 J U_{i} = 30 J d Q = d U + d W d U = d Q - d W U_{f} - U_{i} = d Q - d W U_{f} - 30 = - 20 - (- 8) = - 12 U_{f} = 30 - 12 U_{f} = 18 J 9 x = 18 x = 2$

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