A bicycle tire tube is inflated using a pump. | vedclass

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

Question

(A) In an adiabatic process,the work done $W$ by the gas is given by the formula $W = \frac{P_{i}V_{i} - P_{f}V_{f}}{\gamma - 1}$.Since the volume $V$

Vedclass · Accepted Answer

$\frac{P_{2}V - P_{1}V}{\gamma - 1}$

Vedclass · Answer

(A) In an adiabatic process,the work done $W$ by the gas is given by the formula $W = \frac{P_{i}V_{i} - P_{f}V_{f}}{\gamma - 1}$.Since the volume $V$ of the tube remains constant throughout the process,we have $V_{i} = V_{f} = V$.The initial pressure is $P_{1}$ and the final pressure is $P_{2}$.Substituting these values into the work formula,we get $W = \frac{P_{1}V - P_{2}V}{\gamma - 1}$.However,the work done $ON$ the gas (by the pump) is the negative of the work done $BY$ the gas.Therefore,the work done to increase the pressure is $W_{ext} = -W = -\left(\frac{P_{1}V - P_{2}V}{\gamma - 1}\right) = \frac{P_{2}V - P_{1}V}{\gamma - 1}$.

$A$ bicycle tire tube is inflated using a pump. Assume the volume of the tube $V$ is constant and in each stroke,an amount of air $\Delta V$ is pushed into the tube under an adiabatic process. What is the work done to increase the pressure in the tube from $P_{1}$ to $P_{2}$?

Similar Questions

The volume of an ideal gas $(\gamma=1.5)$ is changed adiabatically from $5 \ L$ to $4 \ L$. The ratio of initial pressure to final pressure is:

$A$ thermodynamic system is compressed adiabatically, then its temperature

In which thermodynamic process is there no exchange of heat between the system and the surroundings?

Assertion $(A)$: When an ideal gas is compressed adiabatically,its temperature and the average kinetic energy of the gas molecules increase.
Reason $(R)$: The kinetic energy increases because of collisions of molecules with the moving parts of the wall.

Vedclass Test Series

Exam Paper Generator

Online Exam Module