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One cubic metre of an ideal gas is at a pressure of $10^{5} N / m^{2}$ and temperature $300 k$ . The gas is allowed to expand at constant pressure to twice its volume by supplying heat. If the change in internal energy in this process is $10^{4} J$ , then the heat supplied is _____

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$10^{5} J$

$10^{4} J$

$11 \times 10^{4} J$

$2.2 \times 10^{5} J$

answer is C.

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Detailed Solution

$PV = nRT = 10^{5} \times 1 = n (831.4) (300)$

$\Rightarrow n = 40 Δ U = n C_{V} d T \Rightarrow C_{V} = 0.8333$

$d Q = n C_{P} d T = n (C_{V} + R) d T = 11 \times 10^{4} J$

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