Question

Work is done on an adiabatic system due to which its velocity changes from 10 m/s to 20 m/s, elevation increases by 20 m and temperature increases by 1 K. The mass of the system is 10 kg $c_v=100J/\left(kgK\right)$ and gravitational accelaration is $10m/s^2$. If there is no change in any other component of the energy of the sysytem, the magnitude of total work done (in kJ) on the system is

• A. 4.5

Answer 1

The correct option is A 4.5
Ist law for process:
$\delta Q=dE+\delta W$
$0=\Delta U+\Delta K.E+\Delta P.E+\delta W$
$0=m{c}_{v}dT+\frac{1}{2}m(V_2^2-V_1^2)$+$mg(z_2-z_1)+W_{1-2}$
$0=10\times 0.1\times$1+$\frac{1}{2}\times 10\left(\right(20{)}^2-\left(10{)}^2\right)\times {10}^3$+10$\times$10$\times$20$\times$${10}^{-3}$$W_{1-2}$
$\therefore$ $W_{1-2}=-4.5kJ$
$=4.5kJ,$ work done on the system.