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

Byju's Answer

Standard XI

Physics

Conduction Law

A monatomic i...

Question

A monatomic ideal gas is contained in a rigid container of volume $V$ with walls of total surface area $A$ , thickness $x$ and thermal conductivity $K$ . The gas is at an initial temperature $T_{o}$ and pressure $P_{o}$ . The temperature of the surrounding air is $T$ . All the temperatures are in absolute scale. If the temperature of the gas at any time $t$ can be expressed as $T (t) = T_{s} - (T_{s} - T_{o}) e^{- λ t}$ , find the pressure of the gas at the steady state condition.

P = P_{o}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

P = 2 P_{o}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

P = \frac{P_{o}}{T_{o}} T_{s}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

None of the above

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C $P = \frac{P_{o}}{T_{o}} T_{s}$
As the process is isochoric, $\frac{P_{o}}{T_{o}} = \frac{P (t)}{T (t)}$
[fixed volume of container]
$∵ T (t) = T_{s} - (T_{s} - T_{o}) e^{- λ t}$
$P (t) = \frac{P_{o}}{T_{o}} [T_{s} - (T_{s} - T_{o}) e^{- λ t}]$
At steady state, as $t \to \infty$ , second term goes to zero.
$\Rightarrow P = \frac{P_{o}}{T_{o}} T_{s}$

Suggest Corrections

Similar questions

Q. One mole of monatomic ideal gas is contained in a rigid container of volume

V

with walls of total surface area

A

, thickness

x

and thermal conductivity

K

. The gas is at an initial temperature

T_{o}

and pressure

P_{o}

. The temperature of the surrounding air is

T_{s}

. All the temperatures are in absolute scale. If the temperature of the gas at any time

t

can be expressed as

T (t) = T_{s} - (T_{s} - T_{o}) e^{- λ t}

, find the value of

λ

Q. A monoatomic ideal gas is contained in a rigid container of volume

V

with walls of total surface area

A

, thickness

x

and thermal conductivity

K

. The gas is at an initial temperature

T_{o}

and pressure

P_{o}

. The temperature of the surrounding air is

T

. All the temperatures are in absolute scale. If the temperature of the gas at any time

t

can be expressed as

T (t) = T_{s} - (T_{s} - T_{o}) e^{- λ t}

, find the pressure of the gas at the steady state condition.

Q. A monoatomic ideal gas is contained in a rigid container of volume

V

with walls of total surface area

A

, thickness

x

and thermal conductivity

K

. The gas is at an initial temperature

T_{o}

and pressure

P_{o}

. The temperature of the surrounding air is

T_{s}

. All the temperatures are in absolute scale. If the temperature of the gas at any time

t

can be expressed as

T (t) = T_{s} - (T_{s} - T_{o}) e^{- λ t}

, find the value of

λ

Q. One mole of a monatomic ideal gas is contained in a rigid container of volume

V_{0}

with walls of total surface area A, thickness x and thermal conductivity K. The gas is at an initial temperature

T_{0}

and pressure

P_{0}

. Find the pressure of the gas as a function of time if the temperature of surrounding air is

T_{s}

. All the temperatures are in absolute scale.

Q. An amount n (in moles) of a monatomic gas at an initial temperature T₀ is enclosed in a cylindrical vessel fitted with a light piston. The surrounding air has a temperature T_s (> T₀) and the atmospheric pressure is P_α. Heat may be conducted between the surrounding and the gas through the bottom of the cylinder. The bottom has a surface area A, thickness x and thermal conductivity K. Assuming all changes to be slow, find the distance moved by the piston in time t.

Join BYJU'S Learning Program

The correct option is C P=PoToTsAs the process is isochoric, PoTo=P(t)T(t) [fixed volume of container] ∵T(t)=Ts−(Ts−To)e−λt P(t)=PoTo[Ts−(Ts−To)e−λt] At steady state, as t→∞, second term goes to zero. ⇒P=PoToTs