A gas under constant pressure of $4.5 \times 10^{5} Pa$ , when subjected to 800 kJ of heat, changes the volume from 0.5 $m^{3}$ to 2.0 $m^{3}$ . The change in internal energy of the gas is

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$1.25 \times 10^{5} J$

$3.25 \times 10^{5} J$

$6.75 \times 10^{5} J$

$5.25 \times 10^{5} J$

answer is D.

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Detailed Solution

$\begin{array}{l} P = 4 .5 \times 10^{5} Pa; dQ = 800 kJ \\ V_{1} = 0 .5 m^{3}; V_{2} = 2 m^{3} \\ dW = P (V_{2} - V_{1}) = 4 .5 \times 10^{5} (2 - 0 .5) \\ = 6 .75 \times 10^{5} J \end{array}$

Change in internal energy

$\begin{matrix} dU = dQ - dW \\ = 800 \times 10^{3} - 6 .75 \times 10^{5} = 1 .25 \times 10^{5} J \end{matrix}$

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