An iron rod of heat capacity C is heated to t | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let the equilibrium temperature be $T$. Since the system is adiabatic,the total heat lost by the iron rod equals the total heat gained by the air

Vedclass · Accepted Answer

$\left( \frac{10C + 7R}{3C + 7R} \right) T_0$

Vedclass · Answer

(D) Let the equilibrium temperature be $T$. Since the system is adiabatic,the total heat lost by the iron rod equals the total heat gained by the air and the vessel-piston assembly.Heat lost by the iron rod = $C(8T_0 - T)$.Heat gained by the vessel and piston = $2C(T - T_0)$.Heat gained by $2$ moles of diatomic gas (at constant pressure,as the piston is movable and atmospheric pressure $P_0$ is constant) = $n C_p (T - T_0) = 2 	imes \frac{7R}{2} (T - T_0) = 7R(T - T_0)$.Equating heat lost and gained: $C(8T_0 - T) = 2C(T - T_0) + 7R(T - T_0)$.$8CT_0 - CT = 2CT - 2CT_0 + 7RT - 7RT_0$.$8CT_0 + 2CT_0 + 7RT_0 = CT + 2CT + 7RT$.$T_0(10C + 7R) = T(3C + 7R)$.$T = \left( \frac{10C + 7R}{3C + 7R} ight) T_0$.

Similar Questions

$A$ thermocouple develops $40\,\mu V/K$. If the hot and cold junctions are at $40\,^{\circ}C$ and $20\,^{\circ}C$ respectively,then the emf developed by a thermopile using $150$ such thermocouples in series shall be ............... $mV$.

$A$ closed bottle containing water at $30^{\circ}C$ is carried to the moon in a spaceship. If it is placed on the surface of the moon,what will happen to the water as soon as the lid is opened?

If $60 \%$ of the kinetic energy of water falling from a $210 \ m$ high waterfall is converted into heat,the rise in temperature of the water at the bottom of the fall is nearly (specific heat of water $= 4.2 \times 10^3 \ J \ kg^{-1} \ K^{-1}$ and $g = 10 \ m/s^2$):

$Assertion :$ In the pressure-temperature $(P-T)$ phase diagram of water,the slope of the melting curve is found to be negative.
$Reason :$ Ice contracts on melting to water.

$A$ closed bottle containing water at $30^{\circ} C$ is opened on the surface of the moon. Then,

Vedclass Test Series

Exam Paper Generator

Online Exam Module