Question

A thermally insulated, closed copper vessel contains water at ${15}^{0}C$. When the vessel is shaken vigorously for $15$ minutes, the temperature rises to ${17}^{0}C$. The mass of the vessel is $100g$ and that of the water is $200g$. The specific heat capacities of copper and water are ${\text{420 J kg}}^{-1}{K}^{-1}$ and ${\text{4200 J kg}}^{-1}{K}^{-1}$ respectively. Neglect any thermal expansion.
(a) How much heat is transferred to the liquid-vessel system?
(b) How much work has been done on this system?
(c) How much is the increase in internal energy of the system?

Answer 1

Given data,

$t_1={15}^{0}C$ $t_2={17}^{0}C$

$\Delta t=t_2-t_1=17{}^{\circ }C-15{}^{\circ }C=2^{0}C=2+273=275K$

$m_v=100g=0.1kg$

$m_w=200g=0.2kg$

$c{u}_g=420J/kg-k$

$W_g=4200J/kg-k$

$a)$ The heat transferred to the liquid vessel system is $0$. The internal heat is shared between the vessel and water.

$b)$ Work done on the system = Heat produced in it.

$\Rightarrow dw=100\times {10}^{-3}\times 420\times 2+200\times {10}^{-3}\times 4200\times 2$

$=84+84\times 20$

$=84\times 21=1764J$

$c)$ $dQ=0,dU=-dW=1764J$. [since $dw=-ve$ work done is converted to heat, So, heat given to liquid is $z$]