2 moles of a monoatomic gas are expanded to double its initial volume, through a process, $\frac{P}{V} = constant$ . If its initial temperature is 300 K, then which of the following is not true.

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Δ T = 900 K

Δ Q = 3200 R

Δ W = 900 R

Δ Q = 3600 R

answer is B.

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Detailed Solution

$P V = n R T g i v e n P V = c o n s tan t n R T V 2 = c o n s tan t T 2 T 1 = 2 V V 2 = 4, T 2 = 4 T 1 T 2 = 4 × 300 K = 1200 K$

$\begin{array}{l} W = \int P d V = \int_{V_{0}}^{2 V_{0}} k V d V = \frac{3}{2} k {V_{0}}^{2} = \frac{3 n R T_{0}}{2} = \frac{3 \times 2 \times R \times 300}{2} = 900 R \\ Δ U = \frac{f}{2} n R (∆ T) = \frac{3}{2} \times 2 \times R \times 900 = 2700 R \\ Δ Q = Δ U + Δ W = 2700 R + 900 R = 3600 R \end{array}$