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Standard XII

Physics

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An ideal gas ...

Question

An ideal gas is taken through a cyclic thermodynamic process through four steps $1, 2, 3, 4$ respectively. The amounts of heat involved in these steps are $Q_{1} = 5960 J, Q_{2} = 5585 J, Q_{3} = - 2980 J$ and $Q_{4} = 3645 J$ respectively. The corresponding quantities of work involved are $W_{1} = 2200 J, W_{2} = 8250 J, W_{3} = - 1100 J$ and $W_{4}$ respectively. The value of $W_{4}$ is

1865 J

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2860 J

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6620 J

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8620 J

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Solution

The correct option is B $2860 J$
In a cyclic process , $Δ U = 0$
$\Rightarrow$ From, first law of thermodynamics
$Q = Δ U + W . . . (i)$
For the cyclic process $Q = Q_{1} + Q_{2} + Q_{3} + Q_{4}$
Net work done in cyclic process is,
$W = W_{1} + W_{2} + W_{3} + W_{4}$
Hence from Eq $(i)$ ,
$Q_{1} + Q_{2} + Q_{3} + Q_{4} = W_{1} + W_{2} + W_{3} + W_{4}$
$\Rightarrow W_{4} = (Q_{1} + Q_{2} + Q_{3} + Q_{4}) - (W_{1} + W_{2} + W_{3})$
$W_{4} = (5960 + 5585 - 2980 + 3645) - (2200 + 8250 - 1100)$
$∴ W_{4} = 2860 J$

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Similar questions

Q. An ideal gas is taken through a cyclic thermodynamic process involving four steps. The amounts of heat involved in these steps are

Q_{1} = 5960 J, Q_{2} = - 5585 J, Q_{3} = - 2980 J

and

Q_{4} = 3645 J

, respectively. The corresponding amounts of work done are

W_{1} = 2200 J, W_{2} = - 825 J

and

W_{3} = - 1100 J

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W_{4} = r e s p e c t i v e l y

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Find the value of

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Q. An ideal gas is taken through a cyclic thermodynamic process through four steps. The amounts of heat involved in these steps are

Q_{1} = 5960 J

Q_{2} = - 5585 J

Q_{3} = - 2980 J

and

Q_{4} = 3645 J

respectively. The corresponding works involved are

W_{1} = 2200 J

W_{2} = - 825 J

W_{3} = - 1100 J

and

W_{4}

respectively.
What is the efficiency of the cycle?

An ideal gas is taken through a cyclic thermodynamic process through four steps. The measures of heat involved in these steps are: $Q_{1} = 5960 J, Q_{2} = - 5585 J, Q_{3} = - 2980 J$ and $Q_{4} = 3645 J,$ respectively. The corresponding quantities of work involved are $W_{1} = 2200 J, = W_{2} = - 825 J$ and $W_{3} = 1100 J$ respectively.

The value of $W_{4}$ ( in $J$ ) is:

(write the absolute value of an answer)

An ideal gas is taken through a cyclic thermodynamical process through four steps $Q_{1}$ = 5960J, $Q_{2}$ = –5585J, $Q_{3}$ = –2980J and $Q_{4}$ = 3645J, respectively. The corresponding works involved are $W_{1} = 2200 J, W_{2} = - 825 J, W_{3} = - 1100 J$ and $W_{4}$ respectively. The value of W4 is: