A resistance coil connected to an external ba | vedclass

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

Question

(D) For an ideal gas,the internal energy depends only on temperature. Since the temperature of the gas remains unchanged,the change in internal energy

Vedclass · Accepted Answer

$\frac{i^2 R}{mg}$

Vedclass · Answer

(D) For an ideal gas,the internal energy depends only on temperature. Since the temperature of the gas remains unchanged,the change in internal energy $\Delta U = 0$.According to the first law of thermodynamics,$\Delta Q = \Delta U + W$. Since $\Delta U = 0$,we have $\Delta Q = W$.The heat supplied by the resistance coil in time $t$ is $\Delta Q = i^2 R t$.The work done by the gas in moving the piston of mass $m$ upward by a distance $x$ is $W = mgx$ (since atmospheric pressure is neglected).Equating the two,we get $i^2 R t = mgx$.Differentiating with respect to time $t$,we get $i^2 R = mg \frac{dx}{dt}$.Since the speed of the piston is $v = \frac{dx}{dt}$,we have $i^2 R = mgv$.Therefore,the speed of the piston is $v = \frac{i^2 R}{mg}$.

Similar Questions

Which of the following statements is incorrect regarding the first law of thermodynamics?

When a system is taken from state $i$ to a state $f$ along path $iaf$,$Q = 50 \, J$ and $W = 20 \, J$. Along path $ibf$,$Q = 35 \, J$. If $W = -13 \, J$ for the curved return path $fi$,$Q$ for this path is ...... $J$.

In changing the state of a thermodynamic system from state $A$ to state $B$, the heat supplied to the system is $Q$ and the work done by the system is $W$. The change in its internal energy is

Vedclass Test Series

Exam Paper Generator

Online Exam Module