Question

A cylinder of mass 1kg is given heat of 20000 J at atmospheric pressure. If initially temperature of cylinder is ${20}^{\circ }C$, then work done by the cylinder will be (Given that Specific heat of cylinder $=400Jk{g}^{-1}$, Coefficient of volume expansion $=9\times {10}^{-5}{}^{\circ }{C}^{-1}$, Atmospheric pressure $={10}^{5}N/m^2$ and density of cylinder 9000 $kg/m^3$)

• A. 0.02 J
• B. 0.05 J
• C. 0.08 J
• D. 0.1 J

Answer 1

The correct option is B 0.05 J

$△Q=mc△T\Rightarrow △T=\frac{20000J}{1kg\times \left(400J/k{g}^{\circ }C\right)}={50}^{\circ }C$
$\Rightarrow T_{Final}={70}^{\circ }C$
Hence $W=P_{atm}△V=P_{atm}{V}_0\gamma △T$
$=\left({10}^{5}N/m^2\right)\left(\frac{1}{9\times {10}^3}{m}^3\right)(9\times {10}^{-5}/{}^{\circ }C)\left({50}^{\circ }C\right)=005J$