An ideal gas ( γ = 5 / 3 ) is adiabatically compressed from 640 cm 3 to 80 cm 3 . If the initial pressure is P , then find the final pressure?

Given, Initial pressure is P Volume at state 1 is V 1 = 640 cm 3 Volume at state 2 is V 2 = 80 cm 3 Ratio of volume at two state is V 1 V 2 = 640 80 = 8 For adiabatic process, Equation of state is given by, P V γ = C … 1 Taking ratio for both state, we have ⇒ P ' P = V 1 V 2 γ , where P ' represents pressure at second state. ⇒ P ' = P 8 5 3 ⇒ P ' = 32 P

In an adiabatic process, the pressure is increased by 2 3 % . If γ = 3 2 , then find the decreases in volume (approximately).

Given, the percentage increase in pressure is, ∆ P P × 100 = 2 3 % , the ratio of specific heat is, γ = 3 2 . The equation of state for adiabatic process is given by, P V γ = C . Taking log on both sides, we have, ⇒ ln P + γ ln V = ln C . Differentiating both sides, we have, ⇒ ∆ P P + γ ∆ V V = 0 ⇒ ∆ V V × 100 = - 1 γ × ∆ P P × 100 ⇒ ∆ V V × 100 = - 1 3 2 × 2 3 ⇒ ∆ V V × 100 = - 4 9 . The percent decrease in volume is 4 9 % .

When the state of a system changes form A to B adiabatically, the work done on the system is 322 J . If the state of the same system is changed from A to B by another process and heat required is 50 calories, then find the work done on the system in this process ( J = 4 . 2 J cal - 1 ) .

The process is adiabatic. It means heat exchange is zero ∆ Q = 0 . The work done on the system, W AB = ∆ W = - 322 , change in internal energy, ∆ U = ? According to first law of thermodynamics, ⇒ ∆ Q = ∆ W + ∆ U 0 = - 322 + ∆ U ∆ U = 322 J Now, ∆ Q 2 = 50 × 4 . 2 = 210 ∆ Q 2 = ∆ W 2 + ∆ U 2 ∆ W 2 = 210 - 322 ∆ W 2 = - 112 J

If Q amount of heat is given to a diatomic ideal gas in a process in which the gas perform a work 2 Q 3 on its surrounding, find the molar heat capacity (in terms of R ) for the process.

We know, Q = n c ∆ T . . . 1 W = 2 Q 3 . Using first law of thermodynamics, d Q = d U + d W d U = Q - 2 Q 3 Q 3 = n c v ∆ T . For diatomic ideal gas, C v = 5 R 2 . So, n ∆ T = 2 Q 15 R . From equation 1 , Q = c × 2 Q 15 R c = 15 R 2 c = 7 . 5 R .

EASY

JEE Main/Advance

IMPORTANT

Earn 100

The pressure and density of a diatomic gas $(γ = \frac{7}{5})$ change adiabatically from $(P, d)$ to $(P^{'}, d^{'}) .$ If $\frac{d^{'}}{d} = 32,$ then find the value of $\frac{P'}{P}$ ?

50% studentsanswered this correctly

Important Questions on Thermodynamics

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 17 - Thermodynamics>Exercise - 1>Q 25

An ideal gas

(γ = 5 / 3)

is adiabatically compressed from

640 {cm}^{3}

80 {cm}^{3}

. If the initial pressure is

P

, then find the final pressure?

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 17 - Thermodynamics>Exercise - 1>Q 26

In an adiabatic process, the pressure is increased by

\frac{2}{3} %

. If

γ = \frac{3}{2}

, then find the decreases in volume (approximately).

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 17 - Thermodynamics>Exercise - 1>Q 27

An ideal gas at pressure

4 \times 10^{5} Pa

and temperature

400 K

occupies

100 cc

. It is adiabatically expanded to double of its original volume. Calculate (a) the final pressure, (b) final temperature, and (c) work done by the gas in the process

(γ = 1.5)

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 17 - Thermodynamics>Exercise - 1>Q 28

In the figure, the walls of the container and the piston are weakly conducting. The initial pressure, volume and temperature of the gas are $200 K Pa, 800 {cm}^{3} and 100 K$ , respectively. Find the pressure and the temperature of the gas if it is $(a)$ slowly compressed $(b)$ suddenly compressed to $200 {cm}^{3} (γ = 1.5)$ .

Question Image

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 17 - Thermodynamics>Exercise - 1>Q 29

When the state of a system changes form

A

B

adiabatically, the work done on the system is

322 J

. If the state of the same system is changed from

A

B

by another process and heat required is

50

calories, then find the work done on the system in this process

(J = 4.2 J {cal}^{- 1})

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 17 - Thermodynamics>Exercise - 1>Q 30

Find the molar heat capacity (in terms of

R

) of a monoatomic ideal gas undergoing the process,

P V^{(\frac{1}{2})} = constant

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 17 - Thermodynamics>Exercise - 1>Q 31

Q

amount of heat is given to a diatomic ideal gas in a process in which the gas perform a work

\frac{2 Q}{3}

on its surrounding, find the molar heat capacity (in terms of

R

) for the process.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 17 - Thermodynamics>Exercise - 1>Q 32

One mole of a gas expands with temperature

T

such that its volume is,

V = k T^{2}

, where

k

is a constant. If the temperature of the gas changes by

60 ° C

, then find the work done by the gas

(R = \frac{25}{3} J {mol}^{- 1} K^{- 1})

The pressure and density of a diatomic gas γ=75 change adiabatically from (P, d) to (P', d'). If d'd=32, then find the value of P' P?

Important Questions on Thermodynamics

Learn and Prepare for any exam you want !

The pressure and density of a diatomic gas $(γ = \frac{7}{5})$ change adiabatically from $(P, d)$ to $(P^{'}, d^{'}) .$ If $\frac{d^{'}}{d} = 32,$ then find the value of $\frac{P'}{P}$ ?