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Q.

A cylinder of mass 1kg is given heat of 20000 J at atmospheric pressure. If initially temperature of cylinder is 20°C, then work done by the cylinder will be (Given that Specific heat of cylinder = 400 J kg^–1, Coefficient of volume expansion = 9 x 10^–5 °C^–1, Atmospheric pressure = 10⁵ N/m² and density of cylinder 9000 kg/m³)

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a

0.02 J

b

0.05 J

c

0.08 J

d

0.1 J

answer is B.

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Detailed Solution

$\Delta Q = mc\Delta T\Rightarrow \Delta T = \frac{{20000J}}{{1kg \times (400J/kg^\circ C)}} = 50^\circ C$
$\Rightarrow$ T_Final = 70°C
$Hence\,\,W = {P_{atm}}\Delta V = {P_{atm}}{V_0}\gamma \,\Delta T$
$= ({10^5}N/{m^2})\,\left( {\frac{1}{{9 \times {{10}^3}}}{m^3}} \right)\,(9 \times {10^{ - 5}}/^\circ C)\,(50^\circ C) = 0.05J$

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A cylinder of mass 1kg is given heat of 20000 J at atmospheric pressure. If initially temperature of cylinder is 20°C, then work done by the cylinder will be (Given that Specific heat of cylinder = 400 J kg–1, Coefficient of volume expansion = 9 x 10–5 °C–1, Atmospheric pressure = 105 N/m2 and density of cylinder 9000 kg/m3)