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Heat and Work

On a TP diagr...

Question

On a TP diagram, two moles of ideal gas perform process AB and CD. If the work done by the gas in the process AB is two times the work done in the process CD then what is the value of $T_{1} / T_{2}$ ?

A

1/2

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B

1

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C

2

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D

4

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Solution

The correct option is C 2
Let slope of line $A C$ is $m_{1}$ & that of line $D B$ is $m_{2}$ .
then,
$K T_{1} = \frac{m_{2}}{m_{1}}$ ( $k$ is constant part)
$\begin{matrix} 2 K T_{2} = \frac{m_{2}}{m_{1}} K T_{1} = 2 K T_{2} \Rightarrow \frac{T_{1}}{T_{2}} = 2 \end{matrix}$
$∴$ Option $C$ is correct.

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