A gas of mass 'm' and molecular weight 'M' is | vedclass

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

Question

(A) Since the gas flow is suddenly stopped in an insulated tube,the process is adiabatic.The kinetic energy of the gas is given by $K.E. = \frac{1}{2}

Vedclass · Accepted Answer

$\frac{2MV^2(\gamma-1)}{R}$

Vedclass · Answer

(A) Since the gas flow is suddenly stopped in an insulated tube,the process is adiabatic.The kinetic energy of the gas is given by $K.E. = \frac{1}{2}m(2V)^2 = 2mV^2$.In an adiabatic process,the work done to compress the gas is equal to the change in internal energy,which is given by $\Delta U = \frac{nR\Delta T}{\gamma-1}$.Since the number of moles $n = \frac{m}{M}$,we have $\Delta U = \frac{mR\Delta T}{M(\gamma-1)}$.Equating the kinetic energy to the change in internal energy:$2mV^2 = \frac{mR\Delta T}{M(\gamma-1)}$.Solving for $\Delta T$:$\Delta T = \frac{2MV^2(\gamma-1)}{R}$.

Similar Questions

An ideal monoatomic gas expands to twice its volume. If the process is isothermal,the magnitude of work done by the gas is $W_i$. If the process is adiabatic,the magnitude of work done by the gas is $W_a$. Which of the following is true?

Which of the following statements is correct?

One mole of a gas expands such that its volume $V$ changes with absolute temperature $T$ in accordance with the relation $V = K T^2$,where $K$ is a constant. If the temperature of the gas changes by $60 \text{ K}$,then the work done by the gas is ($R$ is the universal gas constant).

Two samples of gas $A$ and $B$ are initially at the same pressure and temperature. They are compressed from volume $V$ to $V/2$. If $A$ is compressed isothermally and $B$ is compressed adiabatically,then the final pressure of $A$ is:

$A$ cyclic process $ABCD$ is shown in the given $P-V$ diagram. The $P-T$ diagram that represents the same process is

Vedclass Test Series

Exam Paper Generator

Online Exam Module