MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Ideal Gas Equation

An ideal mono...

Question

An ideal monoatomic gas is enclosed in a non-conducting cylinder having a piston which can move freely. Suddenly the gas is compressed to 1/8 of its initial volume. Find the final pressure and temperature if initial pressure and temperature are $P_{0}$ and $T_{0}$ respectively.

Open in App

Solution

Since process is adiabatic therefore
$P_{0} V^{\frac{5}{3}} = P_{f i n a l} {(\frac{V}{8})}^{\frac{5}{3}} [γ = \frac{C_{P}}{C_{V}} = \frac{5 R}{2} / \frac{3 R}{2} = \frac{5}{3}]$
$P_{f i n a l} = 32 P_{0}$
Since process is adiabatic therefore
$T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1} \Rightarrow T_{0} V_{0}^{2 / 3} = T_{f i n a l} {(\frac{V_{0}}{8})}^{2 / 3} \Rightarrow T = 4 T_{0}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. A monoatomic ideal gas at pressure

P_{0}

is suddenly compressed to

\frac{1}{27}

its initial volume. The final pressure will be:

Q. A gas is enclosed in a cylindrical can fitted with a piston. The walls of the can and the piston are adiabatic. The initial pressure, volume and temperature of the gas are 100 kPa, 400 cm³ and 300 K, respectively. The ratio of the specific heat capacities of the gas, C_p / C_v = 1.5. Find the pressure and the temperature of the gas if it is (a) suddenly compressed (b) slowly compressed to 100 cm³.

Q. A cylindrical container having non conducting walls is partitioned into two equal parts such that the volume of each part is

V_{0}

. A movable non conducting piston is kept between the two parts. Gas on the left is slowly heated so that the gas on right is compressed up to volume

\frac{V_{0}}{8}

. Find pressure and temperature on both sides if the initial pressure and temperature were

P_{0}

T_{0}

respectively. Also, find heat given by the heater to the gas. (number of moles in each part is n)

Q. An ideal monoatomic gas is at pressure

P_{0}

V_{0}

. It is taken to final volume

2 V_{0}

and final pressure

\frac{P_{0}}{2}

in a process which is straight line on

P - V

Q. A monoatomic ideal gas, initially at temperature

T_{1}

, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature

T_{2}

by releasing the piston suddenly. If

L_{1}

L_{2}

are lengths of gas column before and after expansion respectively, then

\frac{T_{1}}{T_{2}}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Adaptive Q18 hint

PHYSICS

Watch in App

explore_more_icon

Explore more

Ideal Gas Equation

Standard X Physics

Join BYJU'S Learning Program

CrossIcon