An ideal gas undergoes a four step cycle as shown in the P − V diagram below. During this cycle, heat is absorbed by the gas in
($\alpha$) steps 1 and 2 ($\beta$) steps 1 and 3
($\gamma$) steps 1 and 4 ($\delta$) steps 2 and 4 Continue reading An ideal gas undergoes a four step cycle …
Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine? ($g=10 m/s^2$)
(1) 10.2 kW
(2) 8.1 kW
(3) 12.3 kW
(4) 7.0 kW Continue reading Water falls from a height of 60 m at the rate of 15 kg/s ….
A cup of coffee cools from $90^{\circ}$C to $80^{\circ}$C in t minutes when the room temperature is $20^{\circ}$C. The time taken by a similar cup of coffee to cool from $80^{\circ}$C to $60^{\circ}$C at the same room temperature $20^{\circ}$C is:
(1) $\frac {13}{10}$t
(2) $\frac {13}{5}$t
(3) $\frac {10}{13}$t
(4) $\frac {5}{13}$t Continue reading A cup of coffee cools from $90^{\circ}$C ….
Due to cold weather a 1 m water pipe of cross-sectional area $1 cm^2$ is filled with ice at $-10^\circ C $. Resistive heating is used to melt the ice. Current of 0.5 A is passed through $4 k\Omega $ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required?
(Given latent heat of fusion for water/ice $=3.33 \times 10^5 J Kg^{-1}$, specific heat of ice $=2\times 10^3 J Kg^{-1}$ and density of ice $=10^3 Kg m^{-3} $ )
(A) 3.53 s
(B) 0.353 s
(C) 35.3 s
(D) 70.65 s
Solution
Electrical Energy = Thermal Energy
$\therefore I^2 Rt = Cm\Delta T + mL = m (C\Delta T + L) $
$\Rightarrow 0.5^2 \times 4000 \times t = \rho V (2 \times 10^3 \times 10 + 3.33 \times 10^5 )$
$\Rightarrow 1000 t = 10^3 \times Al (2 \times 10^4 + 33.3 \times 10^4 )$
$\Rightarrow t = 1 \times 10^{-4} \times 1 (35.3 \times 10^4 ) = 35.3 s $
Answer: (C)
