Question

A vertical cyclinder with heat - conducting with heat conducting walls is closed at the bottom and its fitted with a smooth light piston. It contains one mole of an ideal gas. The temperature of the gas is always equal to the surrounding's temperature $T_o$ . The piston is moved up slowly to increase the volume of the gas to $n$ times. Which of the following is incorrect?

• A. Work done by the gas in $R{T}_o\ln \left(n\right)$.
• B. Work done against the atmosphere is $R{T}_o(n-1).$
• C. There is no change in the internal energy of the gas.
• D. The final presure of the gas is $\frac{1}{n-1}$ times its initial pressure.

Answer 1

Answer: (D)

The final presure of the gas is $\frac{1}{n-1}$ times its initial pressure.

Work Done by gas (isothermal process) :

$W=nRT\ln \left(\frac{V_2}{V_1}\right)=R{T}_o\ln \left(n\right)$

Work Done against Atmosphere (Pressure of atmosphere is constant P & Volume is decreased):

$W=P△V=P(nV-V)=PV(n-1)=R{T}_o(n-1)$

As there is no change in temperature hence no change is Internal Energy (Always in synchronization with atmosphere).

Ideal Gas Equation:

$PV=nRTPV=R{T}_o{P}^{\prime }\left(nV\right)=R{T}_o{P}^{\prime }=\frac{P}{n}$