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Standard XII

Physics

Basic Differentiation Rule

A vertical ho...

Question

A vertical hollow cylinder contains an ideal gas. The gas is enclosed by a $5 k g$ movable piston with area of cross-section $5 \times 10^{- 3} m^{- 2}$ . The gas is heated from $300 t o 350 K$ and the piston rises by $0.1 m$ . The piston is now clamped at this position and the gas is cooled back to $300 K$ . Find the difference between the heat energy added during heating process and energy lost during the cooling process

65 J

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55 J

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75 J

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95 J

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none

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Solution

The correct option is B $55 J$
$(△ Q)_{p} = n C_{p} △ T = △ U + △ W$
When the piston is clamped, volume becomes constant
$∴$ Heat withdrawn, $(△ Q)_{v} = n C_{v} △ T = △ U$
or, $(△ Q)_{p} - (△ Q)_{v} = △ W = P △ V$

$P = [P_{0} + \frac{M g}{A}]$
$△ V = A (0.1)$
$(△ Q)_{p} - (△ Q)_{v} = (P_{0} + \frac{M g}{A}) A (0.1)$
$= 10^{5} \times 5 \times 10^{- 3} + 5 \times 10] (0.1)$
$= 55 J$

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The correct option is B 55J(△Q)p=nCp△T=△U+△WWhen the piston is clamped, volume becomes constant ∴ Heat withdrawn, (△Q)v=nCv△T=△Uor, (△Q)p−(△Q)v=△W=P△VP=[P0+MgA]△V=A(0.1)(△Q)p−(△Q)v=(P0+MgA)A(0.1)=105×5×10−3+5×10](0.1)=55J